纯C3模块

IF 0.5 Q3 MATHEMATICS

Asian-European Journal of Mathematics Pub Date : 2023-10-27 DOI:10.1142/s1793557123502194

Kaushal Gupta, Ashok Ji Gupta

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引用次数: 0

摘要

本文研究了一类模，其中两个不相交和的直和是纯子模也是和。这类模块被认为是[公式:见文本]模块，是[公式:见文本]模块的泛化。【公式:见文】类模块除了纯注入和【公式:见文】类模块外，还包括半简单模块、连续模块、不可分解模块和正则模块。我们针对[公式:见文]模给出了许多环的新表征，即半单环、纯半单环、冯·诺伊曼正则环、诺etherian环、纯遗传环、纯-[公式:见文]-环等。此外，我们还讨论了模的[公式:见文]包络和[公式:见文]覆盖，并引入纯连续模作为连续模的推广，引入纯拟连续模作为拟连续模的推广。

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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Pure C3 Modules

Within the paper, we study the class of modules in which the direct sum of two disjoint summands that is a pure submodule is also a summand. This class of modules is considered [Formula: see text] modules, a generalization of [Formula: see text] modules. In addition to pure-injective and [Formula: see text] modules that belong to the class of [Formula: see text] modules, which also include the semisimple, continuous, indecomposable, and regular modules. We gave new characterizations of many rings in respect of [Formula: see text] modules, namely semisimple rings, pure-semisimple rings, von Neumann regular rings, Noetherian rings, pure-hereditary rings, pure-[Formula: see text]-rings, etc. Moreover, we also discuss the [Formula: see text] envelope and [Formula: see text] cover of a module and introduce the pure continuous modules as the generalization of the continuous modules and also introduce the pure quasi-continuous modules as the generalization of the quasi-continuous modules.

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来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

期刊介绍： Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.