Tensor products and solutions to two homological conjectures for Ulrich modules

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16838

Cleto Miranda-Neto, Thyago Souza

引用次数: 0

Abstract

We address the problem of when the tensor product of two finitely generated modules over a Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular in the original sense from the 80’s. As applications, besides freeness criteria for modules, characterizations of complete intersections, and an Ulrich-based approach to the long-standing Berger’s conjecture, we give simple proofs that two celebrated homological conjectures, namely the Huneke-Wiegand and the Auslander-Reiten problems, are true for the class of Ulrich modules.

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乌尔里希模块的张量积和两个同调猜想的解

我们探讨了科恩-麦考莱局部环上两个有限生成模块的张量积何时是后藤等人广义上的乌尔里希，特别是 80 年代的原初意义上的乌尔里希。作为应用，除了模块的自由性标准、完全交集的特征以及基于乌尔里希的方法来解决长期存在的伯杰猜想之外，我们还给出了两个著名的同调猜想（即胡内克-维根问题和奥斯兰德-雷滕问题）在乌尔里希模块类中为真的简单证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.