Auslander深度不等式的一个推广

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。

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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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