Ulrich模的复杂性和刚性及其应用

IF 0.3 4区数学 Q4 MATHEMATICS Mathematica Scandinavica Pub Date : 2022-01-04 DOI:10.7146/math.scand.a-136499

Souvik Dey, D. Ghosh

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引用次数: 6

摘要

我们分析了Ulrich模块是否可以作为检测模块有限同调维数的测试模块，而不一定是极大CM (Cohen-Macaulay)。证明了CM局部环上的Ulrich模具有最大的复杂度和曲率。利用Ulrich模给出了局部环的各种新的表征。我们证明了局部环上每一个维数$s$的Ulrich模都是$(s+1)$-Tor-rigid-test，而不是一般的$s$ -Tor-rigid(其中$s\ge 1$)。在最小复数CM局部环的变形上，我们也研究了其刚性。

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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Complexity and rigidity of Ulrich modules, and some applications

We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ulrich modules over CM local rings have maximal complexity and curvature. Various new characterizations of local rings are provided in terms of Ulrich modules. We show that every Ulrich module of dimension $s$ over a local ring is $(s+1)$-Tor-rigid-test, but not $s$−Tor-rigid in general (where $s\ge 1$). Over a deformation of a CM local ring of minimal multiplicity, we also study Tor rigidity.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.