The Rational Hull of Modules

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-19 DOI:10.1007/s40840-024-01759-4

Gangyong Lee

引用次数: 0

Abstract

In this paper, we provide several new characterizations of the maximal right ring of quotients of a ring by using the relatively dense property. As a ring is embedded in its maximal right ring of quotients, we show that the endomorphism ring of a module is embedded into that of the rational hull of the module. In particular, we obtain new characterizations of rationally complete modules. The equivalent condition for the rational hull of the direct sum of modules to be the direct sum of the rational hulls of those modules under certain assumption is presented. For a right H-module M where H is a right ring of quotients of a ring R, we provide a sufficient condition under which \(\text {End}_R(M)=\text {End}_H(M)\). Also, we give a condition for the maximal right ring of quotients of the endomorphism ring of a module to be the endomorphism ring of the rational hull of the module.

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模块的有理壳

在本文中，我们利用相对稠密的性质，为一个环的最大右商环提供了几个新的特征。由于一个环嵌入了它的最大右商环，我们证明了一个模块的内态环嵌入了模块的有理全环。特别是，我们得到了有理完全模块的新特征。我们提出了在特定假设条件下，模块直和的有理全环是这些模块有理全环的直和的等价条件。对于一个右 H 模块 M，其中 H 是一个环 R 的商的右环，我们提供了一个充分条件，即 \(text {End}_R(M)=\text {End}_H(M)\).此外，我们还给出了一个条件，即一个模块的内定环的最大右商环是该模块的有理壳的内定环。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.