Gorenstein FP∞-Injective Modules and w-Noetherian Rings

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-12-01 DOI:10.1142/s1005386722000499

Shiqi Xing, Xiaoqiang Luo, Kui Hu

引用次数: 1

Abstract

We study some homological properties of Gorenstein [Formula: see text]-injective modules, and we prove (1) a ring [Formula: see text]is not necessarily coherent if every Gorenstein [Formula: see text]-injective [Formula: see text]-module is injective, and (2) a ring [Formula: see text] is not necessarily coherent if every Gorenstein injective [Formula: see text]-module is injective. In addition, we characterize [Formula: see text]-Noetherian rings in terms of Gorenstein [Formula: see text]-injective modules, and we prove that a ring [Formula: see text] is [Formula: see text]-Noetherian if and only if every GV-torsion-free FP-injective [Formula: see text]-module is Gorenstein [Formula: see text]-injective, if and only if any direct sum of GV-torsion-free FP-injective [Formula: see text]-modules is Gorenstein [Formula: see text]-injective.

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Gorenstein FP∞-内射模与w- noether环

研究了Gorenstein[公式:见文]-内射模的一些同调性质，证明了(1)如果每个Gorenstein[公式:见文]-内射模都是内射模，则环[公式:见文]不一定是内射模;(2)如果每个Gorenstein[公式:见文]-内射模都是内射模，则环[公式:见文]不一定是内射模。此外，我们用Gorenstein[公式:见文]-内射模来刻画[公式:见文]-Noetherian环，并证明一个环[公式:见文]是[公式:见文]-Noetherian当且仅当每个gv -无扭转fp -内射[公式:见文]-模都是Gorenstein[公式:见文]-内射，当且仅当gv -无扭转fp -内射[公式:见文]-模的任何直接和都是Gorenstein[公式:见文]-内射。

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.