Local Cohen–Macaulay DG-Modules

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2023-01-03 DOI:10.1007/s10485-022-09703-y

Xiaoyan Yang, Yanjie Li

引用次数: 0

Abstract

Let A be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations of Gorenstein DG-rings by projective and injective dimensions of DG-modules.

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本地Cohen-Macaulay dg模块

设A是一个有界上同调的交换诺瑟局部dg环。对于恒幅局部Cohen-Macaulay dg -模，我们得到了序列深度的显式表达式，证明了Cohen-Macaulay局部性是稳定的，并给出了局部Cohen-Macaulay dg -环上最大局部Cohen-Macaulay dg -模的几个等价定义。我们还利用dg模的射影维数和内射维数给出了Gorenstein dg环的一些表征。

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

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.