半Abelianπ-正则环结构的研究

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英文篇名：Study on the structures of semi-Abelianπ-regular rings 作者：卢建伟 英文作者：LU Jianwei;Department of Mathematics,Shenyang University of Technology; 关键词：半Abelian环 ; 正交准正则环 ; π-正则环 ; 本原幂等元 英文关键词：semi-Abelian ring;;orthogonal pri-regular ring;;π-regular ring;;primitive idempotent 中文刊名：HZDX 英文刊名：Journal of Zhejiang University(Science Edition) 机构：沈阳工业大学理学院; 出版日期：2015-07-15 出版单位：浙江大学学报(理学版) 年：2015 期：v.42 基金：国家自然科学基金资助项目(61074005) 语种：中文; 页：HZDX201504002 页数：6 CN：04 ISSN：33-1246/N 分类号：10-15

摘要

设R为一个非Abel的半Abelianπ-正则环,证明了下述条件等价:1)R仅有2个极大理想;2)Id(R)-{1}是本原的;3)E(R)={0,1}且对于e∈S0r(R),f∈S0l(R)均有ef=0.进一步证明了如果S0l(R)R与RS0r(R)均为R的极大理想,那么R同构于一个正交准正则环与一个Abelianπ-正则环的亚直接和.
        Assume that theπ-regular ring Ris non-Abelian and semi-Abelian.The following conditions are equivalent:1)there exist just two maximal ideals in R.2)Id(R)-{1}is primitive.3)E(R)={0,1}and ef=0for any e∈S0r(R),f∈S0l(R).Furthermore,supposing that S0l(R)Rand RS0r(R)are both maximal ideals of R,we can prove that R will be isomorphic to the subdirect sum of an orthogonal pri-regular ring and an Abelianπ-regular ring.

引文

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