
752 N.W.2d 588 (2008)
276 Neb. 123
PENNFIELD OIL COMPANY, a Nebraska corporation, Appellee,
v.
W.L. WINSTROM, individually and as personal representative of the Estate of R.W. Winstrom, Appellee, and
Andrew L. Winstrom, Appellant.
No. S-06-1268.
Supreme Court of Nebraska.
July 18, 2008.
*593 David A. Domina and Claudia L. Stringfield-Johnson, of Domina Law Group, P.C., Omaha, and Robert J. Routh, of Cline, Williams, Wright, Johnson & Oldfather, L.L.P., Lincoln, for appellant.
John R. Douglas, Brien M. Welch, Daniel J. Epstein, and David A. Blagg, of Cassem, Tierney, Adams, Gotch & Douglas, Omaha, for appellee W.L. Winstrom.
HEAVICAN, C.J., CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
CONNOLLY, J.

I. SUMMARY
Over the past several years, W.L. Winstrom (Bill) and his son, Andrew Winstrom, have waged war over 8.49 shares of Pennfield Oil Company (Pennfield), a closely held corporation. Pennfield's board of directors consisted of Bill; Sydney Winstrom, Bill's wife and Andrew's mother, and Andrew. This is the second appeal concerning the disputed shares. The battle centered on redemption agreements. Bill is Pennfield's chief executive officer and controlling shareholder. Andrew was Pennfield's president until October 2006. Control of Pennfield hinged upon the disposition of the remaining 8.49 shares in the estate of R.W. Winstrom, Bill's father. Bill inherited the shares and had controlled them as the estate's personal representative. Together with the shares he owns, Bill controlled the majority of shares in Pennfield. If Pennfield had redeemed the estate's 8.49 shares, Andrew would have been the majority shareholder.
In Pennfield Oil Co. v. Winstrom (Pennfield I),[1] Andrew and Pennfield appealed from the district court's order that the estate's shares were not subject to Pennfield's demand for redemption. We reversed. We determined that the shares were subject to a valid demand for redemption. We held, however, that the record failed to show Andrew and Pennfield were equitably entitled to specific performance ordering redemption of the shares. We concluded that the directors had not *594 yet decided whether to waive Pennfield's right of redemption under the repurchase agreement.
This appeal presents a couple of issues: Did our mandate allow the district court on remand to reconsider issues raised by Andrew that the court had decided against him before the first appeal? Did Andrew and Pennfield waive several issues because they failed to raise them in the district court? We conclude that Pennfield's redemption of the estate's shares was not mandatory under our decision in Pennfield I. We further conclude that Andrew has waived his claims that Pennfield could not waive redemption by failing to raise them on appeal in Pennfield I. Because Andrew waived these issues in his first appeal, the district court correctly determined they were not part of our mandate. We affirm.

II. BACKGROUND

1. DIVISION OF PENNFIELD'S SHARES BETWEEN R.W.'S ESTATE, BILL, AND ANDREW
R.W. was one of Pennfield's founders; by 1951, he held all of its 70 outstanding shares. In 1960, R.W. gifted 20 shares each to his sons, W.D. Winstrom (Dean) and Bill. That same year, the three shareholders and their wives signed an agreement regarding disposition of their stock (the 1960 agreement). The 1960 agreement stated that if a shareholder died or wished to dispose of his stock, Pennfield "shall" buy the stock at the book value, to be determined at a shareholders' meeting within 30 days of death or intent to dispose. Pennfield redeemed Dean's 20 shares in 1969. In 1987, R.W. gifted 5.27 shares to Bill, giving Bill a majority interest, or 25.27 shares out of the 50 outstanding shares. R.W. died later in 1987. In his will, R.W. devised all of his Pennfield shares to Bill. R.W. designated Bill as personal representative. Thus, although Bill, as personal representative, did not transfer the estate's shares to himself individually, he controlled all of Pennfield's shares.
In December 1987, Pennfield's board of directors elected to redeem the estate's shares. But the board elected to extend the time for redemption; the financial burden of redeeming them all at once created a financial hardship, and the estate also wished to defer estate tax liability. In June 1988, acting for the estate, himself, and Pennfield, Bill created a new "Restated Stock Repurchase Agreement" (the 1988 agreement). The 1988 agreement, like the 1960 agreement, provided that Pennfield "shall" redeem all the stock of a shareholder upon the shareholder's death or if the shareholder wanted to dispose of his or her shares. But unlike the 1960 agreement, the 1988 agreement did not require the shareholders to determine the shares' book value within 30 days. Instead, it required the parties to agree on a closing date for redeeming the shares within 15 months. When a shareholder died, it required Pennfield to defer redemption until the shareholder's estate had paid all deferred federal estate tax if the shareholder's personal representative requested deferral. In addition  and crucial to this appeal  the 1988 agreement allowed Pennfield to waive redemption of a shareholder's stock in specified circumstances. One circumstance was a shareholder's death when his or her shares had passed to a person who had signed onto the 1988 agreement and was employed by Pennfield. This provision clearly applied to the shares R.W. devised to Bill.
In 1988, Andrew was elected president. In January 1990, he signed on to the 1988 agreement. Later that month, the board redeemed 16.24 shares of the estate's shares and voted to sell 15.89 shares to Andrew, conditioned upon his *595 acceptance of the 1988 agreement. Andrew also signed a separate "Stock Redemption Agreement" (the 1990 agreement). In the 1990 agreement, the parties confirmed and ratified all previous agreements as restated in the 1988 agreement, At this time, Bill held 25.27 shares, the estate held 8.49 shares, and Andrew held 15.89 shares. In 1992, Bill gifted 8.43 shares to Andrew, giving Andrew a total of 24.32 shares and Bill 16.84 shares. But because Bill controlled the estate's 8.49 shares as personal representative of R.W.'s estate, he still controlled the majority of Pennfield's shares.

2. BILL'S ATTEMPTS TO TRANSFER THE SHARES TO HIMSELF
In 1997, Bill attempted to transfer the estate's remaining 8.49 shares to himself. But after Andrew refused to sign the stock certificate, the board tabled the transfer. In December 2000, after the estate made its final estate tax payment, Bill again attempted to transfer the estate's shares to himself. But Andrew again refused to sign the stock certificate. In January 2001, Bill demanded a special meeting of the directors to vote on transferring the shares from the estate to Bill. Afterward, Andrew gave notice that Pennfield was redeeming the estate's remaining shares, effective May 2000. Andrew also directed the filing of this action against Bill before the scheduled special meeting. A week later, Pennfield filed an amended petition, adding Andrew as a defendant. In February, the district court issued a temporary injunction, enjoining Andrew and Bill from transferring the estate's shares.

3. DISTRICT COURT'S 2004 ORDER
Following a bench trial in 2004, the district court ruled that the estate's shares were not subject to redemption. It reasoned that the 1960 agreement controlled at the time of R.W.'s death. Because the board did not hold a shareholders' meeting within the 30-day time limit for valuing the estate's shares, the court concluded that Pennfield had waived its right of redemption. It further found that even if Pennfield had not waived this right, allowing it to redeem the estate's shares would be contrary to the parties' intent to give Bill majority ownership of Pennfield's shares. The court found this intent from the parties' 1960 agreement, R.W.'s gifts of shares to Bill over the years, and R.W.'s will, devising his remaining shares to Bill. It also found that Bill's agreements with Andrew showed that Bill did not intend for Andrew to be the majority shareholder. The court therefore concluded it would be inequitable to require Bill to surrender the estate's shares. In the light of these findings, the court denied "each and every other claim in W.L. and Andrew's counterclaim and cross-claims not specifically addressed herein."

4. THIS COURT'S DECISION IN PENNFIELD I

In Pennfield I, we reversed the district court's ruling that the estate's shares were not subject to redemption. We concluded that even if the board waived redemption under the 1960 agreement, the 1988 agreement controlled. We concluded that the 1988 agreement restated and clarified the earlier agreements and that the parties "were all bound by the 1988 agreement."[2] We further determined that (1) the 1988 agreement anticipated persons other than Bill owning Pennfield stock; (2) the 1988 agreement permitted the redemption of stock held by the estate; and (3) the 1988 agreement was enforceable despite R.W.'s will because R.W. and Bill had signed agreements specifically providing for the redemption of stock if a shareholder died. We also rejected the assignment of errors in Bill's cross-appeal.
*596 But, more important, we also determined that the record failed to show "Pennfield and Andrew [were] equitably entitled to a decree ordering the Estate to surrender the stock for redemption."[3] We stated that the 1988 agreement did not change the requirement in the 1960 agreement that the shareholders meet to determine the shares' book value before redeeming them. We further stated that the board of directors had not yet had the opportunity to consider whether the board should waive redemption under the waiver provision in the 1988 agreement. We concluded:
Pennfield and Andrew are entitled to declaratory relief, establishing that Bill and the Estate are subject to a valid demand for redemption of the stock pursuant to the stock transfer restriction agreements. But the record does not affirmatively show that Pennfield took all the steps necessary to redeem the shares, and it appears that the district court's temporary injunction may have prevented Pennfield's shareholders and board of directors from exercising their duties with respect to the redemption agreements. Thus, we conclude on this record, it would be unjust to decree specific performance of the stock transfer redemption agreements.[4]
We remanded the cause for the district court to grant Pennfield and Andrew declaratory relief consistent with our opinion.

5. PROCEEDINGS FOLLOWING OUR REMAND
On remand, Andrew and Pennfield moved for an order that (1) the 8.49 shares subject to redemption could not be voted at a shareholders' meeting and (2) Bill and Sydney were disqualified from voting on the redemption of the estate's shares because they were not disinterested directors. Bill countered. He moved for an order to dissolve the court's injunction and to require the shareholders and board of directors to meet. The district court overruled Andrew and Pennfield's motion and granted Bill's motion. So when the board met, Bill and Sydney voted to waive Pennfield's right to redeem the estate's shares. Thus, Bill maintained control over the majority of Pennfield's shares. They also voted to (1) transfer the disputed shares from the estate to Bill, (2) terminate Andrew's employment, and (3) disavow Pennfield's lawsuit against Bill.
After this meeting, Andrew moved for a temporary restraining order, injunction, case progression order, and trial date on unresolved issues. Andrew contended that the court had not resolved issues raised in Pennfield's original pleadings because they were "not mature for final adjudication" until the directors' 2006 meeting. Those issues were that Bill and Sydney could not vote on Pennfield's waiver of the estate's shares because of their conflict of interest as directors and because Bill had breached his fiduciary duties to Pennfield. Andrew also alleged that this court had required further proceedings to determine whether Pennfield could waive redemption after the estate made its final payment of federal estate tax. He sought an order enjoining the enforcement of the directors' resolution until the court conducted further proceedings to determine whether Pennfield could waive redemption and whether Bill and Sydney were disqualified from voting.
The district court overruled Andrew's motion. It determined that this court was aware of the issues Andrew and Pennfield had raised in their earlier pleadings. The court interpreted our mandate as not requiring any further proceedings before dissolving its injunction and ordering shareholders' and directors' meetings. It *597 further concluded that the record failed to show Bill would cause irreparable harm to Pennfield. It reasoned that the earlier injunctions had merely caused continuous disputes, which were best resolved by allowing the board to act.

III. ASSIGNMENTS OF ERROR
Andrew assigns, restated, that the district court erred in granting equitable relief to Bill when this court directed equitable relief for Pennfield and Andrew. He also assigns that the court erred in refusing to proceed to trial on previously unresolved claims: (1) whether the disputed 8.49 shares could be voted at the board meeting; (2) whether the board could waive Pennfield's right of redemption under any circumstances; (3) whether Bill and Sydney were interested directors and disqualified to vote on Pennfield's redemption of the shares; and (4) whether the redemption waiver was fair to Pennfield under the conflict of interest statutes for corporations.[5]

IV. STANDARD OF REVIEW
The construction of a mandate issued by an appellate court presents a question of law.[6] On questions of law, we are obligated to reach a conclusion independent of the determination reached by the court below.[7]

V. ANALYSIS

1. PARTIES' CONTENTIONS
Andrew contends that Bill was not entitled to any equitable relief under our mandate in Pennfield I. He contends that the district court therefore failed to comply with our mandate in Pennfield I. He argues the district court ignored our mandate by failing to (1) grant equitable relief to Andrew and Pennfield and (2) complete the case on the "remaining issues" raised by Andrew's and Pennfield's pleadings.
Bill contends that both the pleadings and evidence in Pennfield I placed the issue of Bill and Sydney's alleged interested-director status before the district court. Bill also contends that the court decided those issues against Andrew. He argues that these issues were ripe for appeal in Pennfield I because declaratory judgments are binding on the parties in further adjudication. Bill further argues that Andrew is barred from raising issues now that he could have raised in Pennfield I. Bill contends that Andrew failed to assign the district court's determinations as error and did not ask for rehearing after this court issued its decision. Thus, Bill argues that Andrew is now barred from raising the issues he could have raised in Pennfield I.
Simply put, the issue is whether this court's mandate permitted the district court to consider Andrew's "remaining issues" on remand. After receiving a mandate, a trial court is without power to affect rights and duties outside the scope of the remand from an appellate court.[8] Andrew's "remaining issues" generally fall into three broad categories: claims that he (1) raised to the district court and raised to this court in Pennfield I, (2) raised to the district court but failed to raise to this court in Pennfield I; and (3) failed to raise to the district court or this court in Pennfield I.
In Pennfield I, we directed the district court to grant Pennfield and Andrew declaratory relief consistent with our opinion. *598 When an appellate court's mandate makes its opinion a part thereof by reference, the lower court should examine the opinion with the mandate. This allows the lower court to determine the judgment to be entered or the action to be taken thereon.[9] Thus, we examine our opinion in Pennfield I to determine whether our mandate permitted the district court to consider the "remaining issues" raised by Andrew on remand.

2. JUDICIAL NOTICE OF THE PARTIES' PLEADINGS AND BRIEFS
This appeal requires us to determine whether we implicitly decided in Pennfield I some issues Andrew raises now. We must also decide whether Andrew and Pennfield's failure to raise any issues in Pennfield I waived those issues for further proceedings. To make these determinations, we must review our records of the previous appeals.
A court may judicially notice adjudicative facts, which are not subject to reasonable dispute, at any stage of the proceeding.[10] In interwoven and interdependent cases, we may examine our own records and take judicial notice of the proceedings and judgment in a former action involving one of the parties.[11] We have further held that we may take judicial notice of a document, including briefs filed in an appeal, in a separate but related action concerning the same subject matter in the same court.[12]
In this ongoing battle, this court has previously considered two appeals and two original actions arising out of this dispute. Besides Pennfield I, we have dismissed an interlocutory appeal from the parties' dispute over the retention of counsel to represent Pennfield.[13] We have also denied two original applications for a writ of mandamus.[14] Some of the parties' original pleadings in this action are contained in the transcripts of the related actions. So, we will judicially notice the parties' original pleadings in their related appeals and their appellate briefs filed in Pennfield I.
3. THIS COURT IMPLICITLY DECIDED AGAINST ANDREW ON HIS CLAIMS THAT REDEMPTION UNDER THE 1988 AGREEMENT WAS MANDATORY AND THAT BILL WAS ESTOPPED FROM CLAIMING OTHERWISE
Andrew contends that Pennfield's redemption of the estate's remaining shares was mandatory under the 1988 agreement and that this issue was not decided in Pennfield I. He argues that the 1988 agreement permitted Pennfield to only waive redemption during the federal tax deferral period. Andrew and Pennfield raised this argument to the district court and this court in Pennfield I. Andrew contends that our opinion indicates we agreed redemption was mandatory under the 1988 agreement. He concludes that this court's mandate required only that the shareholders determine the shares' book value on remand. We disagree.
We did not make the statements in Pennfield I that Andrew attributes to us. Instead, we pointed out facts that demonstrated the district court's error in relying solely on the 1960 agreement to determine *599 that Pennfield had waived its right of redemption. As noted, we reasoned that the parties had modified the 1960 agreement by the 1988 agreement. We pointed out that Pennfield's deferred redemption of the estate's shares was only permitted under the 1988 agreement. We further stated that "it is plain from the 1988 agreement that it was intended to apply to the shares that were, at that time, held by R.W.'s estate" and that Pennfield's right to waive redemption had been extended by the 1988 agreement.[15] We did not state that Pennfield's right to waive redemption of the estate's shares was limited to the tax deferral period. More important, Andrew's argument that we recognized Pennfield's redemption of the shares was mandatory is inconsistent with our holding. In Pennfield I, we held that Andrew and Pennfield were not entitled to a decree of specific performance requiring Bill to transfer the estate's shares to Pennfield for redemption. Because we rejected Andrew and Pennfield's claim that they were entitled to this specific performance, redemption was not mandatory.
In their Pennfield I briefs, the main thrust of Andrew's and Pennfield's arguments was that Pennfield's redemption of the estate's remaining shares was mandatory under the 1988 agreement. While recognizing that the estate had made its final estate tax payment in 2000, we still denied specific performance. We concluded, in part: "[T]he record indicates that the redemption was not authorized by the board of directors, nor was the board of directors permitted to consider whether redemption should be waived pursuant to the waiver provision of the 1988 agreement."[16] Thus, we implicitly concluded that redemption of the estate's remaining shares was not mandatory under the 1988 agreement.
Bill created the 1988 agreement after Pennfield had elected to redeem the estate's shares over an extended period because of the financial hardship of redeeming them all at once. Despite this election, however, subsection 4(a) of the waiver provision applied to the shares R.W. had devised to Bill. The 1988 agreement did not preclude the board of directors from waiving Pennfield's right to redeem the estate's remaining shares.
Moreover, even if we had incorrectly concluded in Pennfield I that redemption was not mandatory, Pennfield and Andrew did not move for a rehearing. Under the law-of-the-case doctrine, an appellate court's holdings on issues presented to it conclusively settle all matters ruled upon, either expressly or by necessary implication.[17] So, our conclusion that Pennfield's redemption of the estate's remaining shares was not mandatory under the 1988 agreement was a final decision and the law of the case. It was not an issue for the district court to decide on remand.
4. ISSUES THAT ANDREW RAISED TO THE DISTRICT COURT BUT FAILED TO APPEAL WERE WAIVED ON APPEAL AND NOT PART OF OUR MANDATE ON REMAND
Andrew also contends that whether Bill and Sydney had a conflict of interest that precluded them from voting on Pennfield's right to waive redemption was not an issue before this court in Pennfield I. He argues that the district court had not yet decided the issues and that these issues were ripe for adjudication only on remand. For support, Andrew culls this sentence from Pennfield I: "Whether *600 Pennfield can waive redemption under the 1988 agreement is not an issue in this appeal, given the record before us."[18] Andrew argues that this sentence shows our mandate required the district court to determine on remand whether waiver was permissible and, if so, whether Bill and Sydney could vote to waive redemption of the estate's shares.
We agree that the disqualification issues were not before us in Pennfield I. But we do not agree that the statement Andrew relies upon allowed him to relitigate issues that the district court decided against him in its 2004 order. The above statement merely reflects our recognition that the directors had not yet taken action on Pennfield's right to waive redemption at the time we decided Pennfield I. Initially, the directors had tabled Bill's 1997 attempt to transfer the stock to himself after Andrew refused to sign the stock certificate. Later, Andrew's filing of this action after Bill's second attempt to transfer the stock had prevented the directors from voting on the waiver of redemption. Consequently, the result of a directors' vote on the waiver was not certain when we decided Pennfield I. We first stated: "[T]he record reflects that while a waiver of Pennfield's right to redeem was prepared, none has been adopted."[19] Our second statement  "Whether Pennfield can waive redemption under the 1988 agreement is not an issue in this appeal, given the record before us"[20]  was made in the context of rejecting Bill's argument regarding construction of the 1988 agreement. In other words, the issue we concluded was not before us in Pennfield I was that of Pennfield's legal rights under the 1988 agreement  not Bill and Sydney's right to vote on the disputed shares. We conclude that the statement does not support Andrew's argument that we remanded for the district court to reconsider whether Bill and Sydney had a conflict of interest. We could not have remanded the cause for this reason because Pennfield and Andrew did not raise these issues on appeal.

(a) Andrew and Pennfield Raised Bill's and Sydney's Alleged Disqualification to the District Court
The original pleadings show that before the district court issued its 2004 order, Pennfield and Andrew raised the specific issues that they now contend the district court never decided.
One of the claims in Pennfield's original and amended complaint was that Bill's attempt to transfer the shares to himself had violated his fiduciary duty to Pennfield. Pennfield sought a temporary and permanent injunction preventing Bill from taking any action regarding Pennfield's right to redeem the estate's shares.
Andrew made the same allegations in his original and amended counterclaim against Pennfield and in his crossclaim against Bill. Like Pennfield, he also sought a temporary and permanent injunction preventing Bill from taking any action regarding Pennfield's right to redeem the estate's shares. In addition, Andrew specifically alleged that Bill's acts constituted an unlawful preference of Bill's personal interests over Pennfield's best interests, that Bill and Sydney were not disinterested directors, and that Andrew was the only independent director who could act regarding Pennfield's rights in the 1988 agreement. Andrew joined Pennfield's requests for relief. In addition, he sought a declaration that Bill's actions were self-dealing and taken in bad faith.
As noted, in the district court's 2004 order, it concluded that Pennfield had *601 waived its right to redeem R.W.'s shares under the 1960 agreement. It reasoned that allowing Pennfield to redeem them would be inconsistent with R.W. and Bill's intent that Bill would remain the majority shareholder. The court denied Andrew's other claims regarding Bill and Sydney's conflicts of interest.
In Pennfield I, Andrew and Pennfield did not assign as error the district court's overruling of their claims that (1) Bill should be enjoined from taking any action regarding the estate's shares because he had breached his fiduciary duties to Pennfield or (2) Bill and Sydney had conflicts of interest that disqualified them from voting on the waiver.
Andrew and Pennfield's failure to assign as the error the district court's adverse rulings on these issues was perhaps a tactical decision. As noted, in Pennfield I, they mainly argued that redemption of the estate's shares was mandatory. Raising on appeal Bill's and Sydney's alleged disqualification to vote on the redemption would have arguably been a concession that redemption was not mandatory. But, as discussed below, they are now bound by their failure to raise alternative arguments on issues that the district court decided against them.

(b) Andrew Has Waived Disqualification Issues Under the Law-of-the-Case Doctrine
The law-of-the-case doctrine reflects the principle that an issue that has been litigated and decided in one stage of a case should not be relitigated in a later stage.[21] The doctrine promotes judicial efficiency and protects parties' settled expectations by preventing parties from relitigating settled issues within a single action.[22] The doctrine applies with greatest force when an appellate court remands a case to an inferior tribunal.[23] Upon remand, a district court may not render a judgment or take action apart from that which the appellate court's mandate directs or permits.[24]
Under the mandate branch of the law-of-the-case doctrine, a well-recognized waiver rule has emerged:
[A] decision made at a previous stage of litigation, which could have been challenged in the ensuing appeal but was not, becomes the law of the case; the parties are deemed to have waived the right to challenge that decision, for "[i]t would be absurd that a party who has chosen not to argue a point on a first appeal should stand better as regards the law of the case than one who had argued and lost."[25]
An issue is not considered waived if a party did not have both an opportunity and an incentive to raise it in a previous appeal.[26] But this condition was satisfied as Andrew clearly had incentive to raise the disqualification issues in Pennfield I after the district court ruled against him on these claims. Also, we have recognized that an exception to the law-of-the-case doctrine applies if a party shows a material and substantial difference in the *602 facts on a matter previously addressed by an appellate court.[27] But Andrew did not allege any new facts to support his claims, and we need not decide whether to apply any exceptions here because Andrew did not raise any to the district court.

(c) Incidental Arguments on Appeal Are Insufficient to Raise a Claim That the Trial Court Erred
We recognize that Andrew argued on appeal in Pennfield I that because of Bill's self-interest, the court erred in failing to put the burden on Bill to prove that waiver would not harm Pennfield. But this argument was firmly tethered to Andrew's assignment that the district court "[i]mposed the burden-of-proof on the wrong party." He did not argue or assign as error the court's failure to (1) find that Bill and Sydney were disqualified from voting on the waiver or (2) declare Bill's actions were taken for purposes of self-dealing. Thus, we would not have addressed these issues. And the tangential nature of his burden-of-proof argument does not change our conclusion that he waived the disqualification issues by failing to raise them in his first appeal. A point incidentally raised, vaguely referred to, or given cursory treatment on appeal is insufficient to presume an unassigned error.[28]
In sum, an appellant waives claims that were decided against it by the trial court if the appellant elects not to raise those issues on appeal. And the appellant cannot preserve those issues for further proceedings by indirect references to the claims. Because Andrew and Pennfield waived the disqualification issues, they were not part of our mandate on remand.

5. ANDREW FAILED TO RAISE TO THE DISTRICT COURT ALTERNATIVE THEORIES OF ESTOPPEL AGAINST BILL
Andrew also contends that Bill is estopped from enforcing Pennfield's right to waive redemption because he breached the agreement by attempting to transfer shares to himself without first obtaining Pennfield's waiver. Andrew also claims that Bill's actions were inconsistent with waiver by failing to call a directors' meeting to waive redemption until 2001. These arguments are different from Andrew's claim in his original pleadings that Bill's statements to third parties that were inconsistent with waiver estopped him from preventing Pennfield's redemption of the shares. But they are not arguments based on new evidence. They seem to be different theories of estoppel that Andrew failed to raise to the district court in Pennfield I. In addition, he did not raise these arguments to the district court on remand. An appellate court will not consider an issue on appeal that the trial court has not decided.[29]

6. ALL THE ISSUES RAISED BY ANDREW ON REMAND WERE JUSTICIABLE IN PENNFIELD I

We reject Andrew's claims that his "remaining issues" were not ripe for adjudication until after our remand in Pennfield I.
Ripeness is a justiciability doctrine that courts consider in determining whether they may properly decide a controversy.[30] The fundamental principle of *603 ripeness is that courts should avoid entangling themselves, through premature adjudication, in abstract disagreements based on contingent future events that may not occur at all or may not occur as anticipated.[31] Generally, a case is ripe when no further factual development is necessary to clarify a concrete legal dispute susceptible to specific judicial relief, as distinguished from an advisory opinion regarding contingent future events.[32]
Andrew's claims that Bill had breached a fiduciary duty to Pennfield and that Bill and Sydney could not vote on Pennfield's waiver were based on undisputed facts  not contingent future events. In Pennfield I, we specifically stated that "Andrew's cross-claims, and Bill and his wife's petition in intervention, effectively raised the same issues, so the court had before it all the parties to a legal dispute that was ripe for disposition."[33] Andrew clearly raised these issues in his original pleadings. He specifically alleged that his claims were ripe for declaratory judgment, and obtained a judgment.[34] Similarly, Andrew's additional claims that Bill was not entitled to enforce the waiver provision could have been raised to the district court in the first proceeding.
The law disfavors piecemeal appeals. Multiple appeals interfere with efficient judicial administration and impose on the parties costs and risks associated with protracted litigation.[35] We reject Andrew's arguments that his remaining issues were not "mature" for adjudication until after we had decided Pennfield I. Absent allegations of a material and substantial difference in the evidence, issues that the district court decided against Andrew that he failed to appeal, and justiciable issues that Andrew failed to raise to the district court in Pennfield I, were not open to consideration as part of our remand.[36]

7. THE DISTRICT COURT CORRECTLY CONCLUDED THAT OUR MANDATE DID NOT REOPEN WAIVED ISSUES
Our mandate was not broad enough for the district court to permit Andrew to relitigate the issues he had waived on appeal. Although we recognized in Pennfield I that "Andrew filed an answer and cross-claims, generally alleging breaches of contract and fiduciary duties by Bill,"[37] we did not remand for a new trial, further proceedings, or reconsideration of these issues.[38]
*604 We conclude that the district court correctly interpreted our mandate from Pennfield I when our instructions are read with the opinion. We instructed the court to grant Andrew and Pennfield declaratory relief "establishing that Bill and the Estate are subject to a valid demand for redemption of the [estate's] stock."[39] The term "subject to" in this context simply meant "liable to" a valid demand for redemption. Our opinion raised specific conditions that must be satisfied before a demand for redemption could be deemed valid:
[T]he record does not affirmatively show that Pennfield took all the steps necessary to redeem the shares, and it appears that the district court's temporary injunction may have prevented Pennfield's shareholders and board of directors from exercising their duties with respect to the redemption agreements. Thus, we conclude on this record, it would be unjust to decree specific performance of the stock transfer redemption agreements.[40]
As set out in our opinion, those conditions or necessary steps included a shareholders' meeting to determine the book value of the estate's shares. They also included a requirement that the directors meet to "consider whether redemption should be waived pursuant to the waiver provision of the 1988 agreement."[41]
Our opinion required the district court to dissolve its injunction so that Pennfield would have an opportunity to take all the necessary steps for making a valid demand for redemption of the estate's shares. After the directors voted to waive redemption, of course, there could not be a valid demand for redemption. But there was no further action required by our mandate, and the district court's authority on remand was limited to these requirements. The court did not err in concluding that our mandate did not permit it to consider the additional issues raised by Andrew on remand.

VI. CONCLUSION
We conclude that we implicitly decided in Pennfield I that Pennfield's redemption of the shares in R.W.'s estate was not mandatory. Although we held that the shares were subject to Pennfield's valid demand for redemption, we also set out conditions for a valid demand. We remanded the cause to give the board of directors an opportunity to vote on whether to waive Pennfield's right to redeem the estate's shares and to give the shareholders an opportunity to determine the shares' book value. The district court did not err in concluding that our mandate required it to dissolve its prior injunction, which injunction had prevented the directors from voting, and to allow the waiver vote to take place.
We reject Andrew's contention that our mandate required the district court to consider Andrew's further claims for preventing the directors' vote on the waiver. We conclude that Andrew and Pennfield waived all claims decided in the district court's 2004 order that they failed to raise on appeal in Pennfield I. Because those issues were waived on appeal, they were not part of our mandate on remand to the district court.
AFFIRMED.
WRIGHT, J., not participating.
NOTES
[1]  Pennfield Oil Co. v. Winstrom, 272 Neb. 219, 720 N.W.2d 886 (2006).
[2]  Id. at 228, 720 N.W.2d at 896.
[3]  Id. at 239, 720 N.W.2d at 903.
[4]  Id. at 239-40, 720 N.W.2d at 903.
[5]  See Neb.Rev.Stat. § 21-20,112 et seq. (Reissue 1997).
[6]  See Pursley v. Pursley, 261 Neb. 478, 623 N.W.2d 651 (2001).
[7]  Id.
[8]  See VanHorn v. Nebraska State Racing Comm., 273 Neb. 737, 732 N.W.2d 651 (2007).
[9]  See Pursley, supra note 6.
[10]  See, Neb. Evid. R. 201; Neb.Rev.Stat. § 27-201 (Reissue 1995); J.B. Contracting Servs. v. Universal Surety Co., 261 Neb. 586, 624 N.W.2d 13 (2001).
[11]  See Jessen v. Jessen, 259 Neb. 644, 611 N.W.2d 834 (2000).
[12]  Id.
[13]  See Pennfield Oil Co. v. Winstrom, 267 Neb. 288, 673 N.W.2d 558 (2004).
[14]  See id. (discussing parties' filing of original actions).
[15]  Pennfield I, supra note 1, 272 Neb. at 229, 720 N.W.2d at 896.
[16]  Id. at 239, 720 N.W.2d at 903.
[17]  See New Tek Mfg. v. Beehner, 275 Neb. 951, 751 N.W.2d 135 (2008).
[18]  Pennfield I, supra note 1, 272 Neb. at 229, 720 N.W.2d at 897.
[19]  Id. at 229, 720 N.W.2d at 896-97.
[20]  Id. at 229, 720 N.W.2d at 897.
[21]  See New Tek Mfg., supra note 17.
[22]  See Money v. Tyrrell Flowers, 275 Neb. 602, 748 N.W.2d 49 (2008).
[23]  See id.
[24]  See VanHorn, supra note 8.
[25]  County of Suffolk v. Stone & Webster Engineering, 106 F.3d 1112, 1117 (2d Cir.1997), quoting Fogel v. Chestnutt, 668 F.2d 100 (2d Cir.1981). Accord, Amado v. Microsoft Corp., 517 F.3d 1353 (Fed.Cir.2008); Nagle v. Alspach, 8 F.3d 141 (3d Cir.1993); Doe v. Chao, 511 F.3d 461 (4th Cir.2007); U.S. v. Still, 102 F.3d 118 (5th Cir.1996); U.S. v. Adesida, 129 F.3d 846 (6th Cir.1997); Pope v. Ransdell, 251 Kan. 112, 833 P.2d 965 (1992).
[26]  See U.S. v. Quintieri, 306 F.3d 1217 (2d Cir.2002).
[27]  See, Latenser v. Intercessors of the Lamb, Inc., 250 Neb. 789, 553 N.W.2d 458 (1996); Schuelke v. Wilson, 255 Neb. 726, 587 N.W.2d 369 (1998).
[28]  See, McDonald v. Trihub, 173 P.3d 416 (Alaska 2007); McKissick v. Frye, 255 Kan. 566, 876 P.2d 1371 (1994).
[29]  See Clark v. Clark, 275 Neb. 276, 746 N.W.2d 132 (2008).
[30]  See Nebraska Coalition for Ed. Equity v. Heineman, 273 Neb. 531, 731 N.W.2d 164 (2007).
[31]  See, Thomas v. Union Carbide Agric. Products Co., 473 U.S. 568, 105 S.Ct. 3325, 87 L.Ed.2d 409. 473 U.S. 568, 105 S.Ct. 3325, 87 L.Ed.2d 409. 473 U.S. 568, 105 S.Ct. 3325, 87 L.Ed.2d 409 (1985); Texas v. United States, 523 U.S. 296, 118 S.Ct. 1257, 140 L.Ed.2d 406 (1998); Bonge v. County of Madison, 253 Neb. 903, 573 N.W.2d 448 (1998).
[32]  See, Texas v. United States, supra note 31; Aetna Life Ins. Co. v. Haworth, 300 U.S. 227, 57 S.Ct. 461, 81 L.Ed. 617. 300 U.S. 227, 57 S.Ct. 461, 81 L.Ed. 617. 300 U.S. 227, 57 S.Ct. 461, 81 L.Ed. 617 (1937); Public Citizen v. Department of State, 276 F.3d 634 (D.C.Cir. 2002).
[33]  Pennfield I, supra note 1, 272 Neb. at 235, 720 N.W.2d at 900-01 (emphasis supplied).
[34]  Compare Central Neb. Pub. Power v. Jeffrey Lake Dev., 267 Neb. 997, 679 N.W.2d 235 (2004).
[35]  See, e.g., Cerny v. Todco Barricade Co., 273 Neb. 800, 733 N.W.2d 877 (2007); Smith v. Lincoln Meadows Homeowners Assn., 267 Neb. 849, 678 N.W.2d 726 (2004).
[36]  See, generally, 18B Charles Alan Wright, Arthur R. Miller & Edward H. Cooper, Federal Practice and Procedure § 4478.6 (2d ed. 2002).
[37]  Pennfield I, supra note 1, 272 Neb. at 225, 720 N.W.2d at 894.
[38]  Compare, McLeay v. Bergan Mercy Health Sys., 271 Neb. 602, 714 N.W.2d 7 (2006); McKinstry v. County of Cass. 241 Neb. 444, 488 N.W.2d 552 (1992).
[39]  Pennfield I, supra note 1. 272 Neb. at 239, 720 N.W.2d at 903.
[40]  Id. at 239-40, 720 N.W.2d at 903.
[41]  Id. at 239, 720 N.W.2d at 903.
