琐环扩展上的扭转对和相关模块

IF 0.7 4区数学 Q2 MATHEMATICS Hacettepe Journal of Mathematics and Statistics Pub Date : 2024-01-10 DOI:10.15672/hujms.1272122

Lixin Mao

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引用次数: 0

摘要

让 $R\ltimes M$ 是由 $R$-$R$ 双模块 $M$ 构成的环 $R$ 的琐细扩展。我们首先研究如何从 $R$ 上的扭转对构造 $R\ltimes M$ 上的扭转对。我们得到了相对于 $R/ltimes M$ 上的扭转对的有限生成（呈现）模块、平模块和相干环的一些特征。然后，我们讨论了在 $R\ltimes M$ 上的扭转对向 $R$ 的转移。最后，我们给出了一些在莫里塔上下文环中的应用。

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Torsion pairs and related modules over trivial ring extensions

Let $R\ltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$. We first study how to construct torsion pairs over $R\ltimes M$ from torsion pairs over $R$. Some characterizations of finitely generated (presented) modules, flat modules and coherent rings relative to a torsion pair over $R\ltimes M$ are obtained. Then we discuss the transfers of torsion pairs over $R\ltimes M$ to $R$. Finally, some applications are given in Morita context rings.

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来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.