Restricted Injective Dimensions over Cohen-Macaulay Rings

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-03-19 DOI:10.1007/s10468-024-10262-0

Michal Hrbek, Giovanna Le Gros

引用次数: 0

Abstract

We show that the small and large restricted injective dimensions coincide for Cohen-Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of Sather-Wagstaff and Totushek, we suggest a new definition of Cohen-Macaulay Hom injective dimension. We show that the class of Cohen-Macaulay Hom injective modules is the right constituent of a perfect cotorsion pair. Our approach relies on tilting theory, and in particular, on the explicit construction of the tilting module inducing the minimal tilting class recently obtained in (Hrbek et al. 2022).

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科恩-麦考莱环上的限制注入维数

我们证明，对于有限克鲁尔维度的科恩-马科莱环，小限制注入维度和大限制注入维度是重合的。在此基础上，受 Sather-Wagstaff 和 Totushek 近期研究的启发，我们提出了科恩-马科莱同注维的新定义。我们证明了科恩-麦考莱荷姆注入模块类是完美扭转对的右成分。我们的方法依赖于倾斜理论，特别是最近在（Hrbek et al.）

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.