GENERALIZATIONS OF C3 MODULES AND C4 MODULES

IF 0.2 4区数学 Q4 MATHEMATICS

Mathematical Reports Pub Date : 2022-01-01 DOI:10.59277/mrar.2023.25.75.1.187

Zhanmin Zhu

引用次数: 2

Abstract

"Let A be a class of right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A -C3 if, whenever N and K are direct summands of M with N ∩K = 0 and K ∈ A , then N ⊕K is also a direct summand of M; M is called an A -C4 module, if whenever M = A⊕B where A and B are submodules of M and A ∈ A , then every monomorphism f : A → B splits. Some characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple artinian rings, right V-rings, quasi-Frobenius rings and von Neumann regular rings are given."

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c3模块和c4模块的推广

"设A是一类在同构下闭合的右r模，设M是一个右r模。则M称为A -C3，当N和K是M的N∩K = 0且K∈A的直接和时，则N⊕K也是M的直接和;M称为A -C4模，如果当M = A⊕B且A和B是M和A∈A的子模时，则每个单态f: A→B分裂。研究了这类模块的一些表征和性质。作为应用，给出了半单环、右v环、拟frobenius环和von Neumann正则环的一些新的性质。

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

Mathematical Reports MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500. Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.