A -D3 Modules and A -D4 Modules

IF 0.7 Q2 MATHEMATICS
Zhanmin Zhu
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引用次数: 0

Abstract

Let A be a class of some right R -modules that is closed under isomorphisms, and let M be a right R -module. Then M is called A -D3 if, whenever N and K are direct summands of M with M = N + K and M / K A , then N K is also a direct summand of M ; M is called an A -D4 module, if whenever M = B A where B and A are submodules of M and A A , then every epimorphism f : B A splits. Several characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple Artinian rings, quasi-Frobenius rings, von Neumann regular rings, semiregular rings, perfect rings, semiperfect rings, hereditary rings, semihereditary rings, and PP rings are given.
A -D3模块和A -D4模块
设A是一个在同构下封闭的右R模的类,设M是一个右R模。M称为A -D3,如果,当N和K是M的直接和M = N + K和M / K∈A,则N∩K也是M的直接和;M称为A -D4模块,如果M = B⊕A,其中B和A是M和的子模块A∈A,则每个上射f: B ? A分裂。研究了这类模块的若干表征和性质。作为应用,给出了半单Artinian环、拟frobenius环、von Neumann正则环、半正则环、完美环、半完美环、遗传环、半遗传环和PP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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