Gorenstein-Projective Modules over Morita Rings

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2021-09-01 DOI:10.1142/S1005386721000407

Dadi Asefa

引用次数: 2

Abstract

Let [Formula: see text] be a Morita ring which is an Artin algebra. In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring [Formula: see text] and the algebras [Formula: see text] and [Formula: see text]. We prove that if [Formula: see text] is a Gorenstein algebra and both [Formula: see text] and [Formula: see text] (resp., both [Formula: see text] and [Formula: see text]) have finite projective dimension, then [Formula: see text] (resp., [Formula: see text]) is a Gorenstein algebra. We also discuss when the CM-freeness and the CM-finiteness of a Morita ring [Formula: see text] is inherited by the algebras [Formula: see text] and [Formula: see text].

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Morita环上的投影模

设[公式:见文]是一个森田环，它是一个阿廷代数。本文研究了Morita环上的gorenstein -射影模[公式:见文]与代数[公式:见文]和[公式:见文]之间的关系。我们证明了如果[公式:见文]是一个Gorenstein代数，并且[公式:见文]和[公式:见文]都是(见文)。，[公式:见文]和[公式:见文])都有有限的射影维度，那么[公式:见文](见文)。(公式:见原文)是一个戈伦斯坦代数。我们还讨论了Morita环[公式:见文]的cm -自由性和cm -有限性何时被代数[公式:见文]和[公式:见文]继承。

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

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.