Auslander深度不等式的一个推广

IF 0.6 4区数学 Q3 MATHEMATICS

Taiwanese Journal of Mathematics Pub Date : 2021-08-18 DOI:10.11650/tjm/220501

Olgur Celikbas, U. Le, H. Matsui

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引用次数: 1

摘要

在本文中，我们考虑了Auslander的一个深度不等式，它适用于交换Noetherian局部环上的有限生成Tor刚性模。我们提出了这样一个深度不等式是否可以推广到$n$-Tor刚性模的问题，并得到了一般自由的2-Tor刚性模的肯定答案。此外，在附录中，我们使用Dao的eta函数，确定了超曲面上的Tor刚性模的新类，这些新类是非分枝正则局部环的商。

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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An Extension of a Depth Inequality of Auslander

In this paper, we consider a depth inequality of Auslander which holds for finitely generated Tor-rigid modules over commutative Noetherian local rings. We raise the question of whether such a depth inequality can be extended for $n$-Tor-rigid modules, and obtain an affirmative answer for 2-Tor-rigid modules that are generically free. Furthermore, in the appendix, we use Dao's eta function and determine new classes of Tor-rigid modules over hypersurfaces that are quotient of unramified regular local rings.

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来源期刊

Taiwanese Journal of Mathematics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.