On the Triviality of Gorenstein $$(\mathcal {L}, \mathcal {A})$$ -Modules

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-04-26 DOI:10.1007/s41980-024-00871-2

Xinxin Wang

引用次数: 0

Abstract

Let $(\mathcal {L}, \mathcal {A})$ be a bi-complete duality pair. We consider when the relative Gorenstein modules with respect to such a duality pair coincide with the classical homological modules. As applications, we characterize (weak) global dimension via such a duality pair, characterize strongly CM-freeness of flat-typed $(\mathcal {L}, \mathcal {A})$-Gorenstein rings and obtain the compactly-generatedness of some relative derived categories. Applying the results into frequent duality pairs, our results unify the corresponding results for Gorenstein AC-modules and Ding modules.

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论戈伦斯坦 $$(\mathcal {L}, \mathcal {A})$$ - 模块的琐碎性

让 $(\mathcal {L}, \mathcal {A})$ 是一个双完全对偶。我们将考虑与这样的对偶对相关的相对戈伦斯坦模块与经典同调模块重合的情况。作为应用，我们通过这样的对偶对描述了（弱）全局维度，描述了平（(\mathcal {L}, \mathcal {A})\)-戈伦斯坦环的强CM-无穷性，并得到了一些相对派生类的紧凑生成性。把这些结果应用到频繁对偶对中，我们的结果统一了戈伦斯坦交流模块和丁模块的相应结果。

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

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.