关于单位π-正则环的一个注(英文)  

A Note on the Unit π-Regular Rings

作　　者：储茂权[1] 徐学海[1] 干玥[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2012年第6期511-513,共3页Journal of Anhui Normal University(Natural Science)

基　　金：Supported by Natural Science of Education Department of Anhui Province(KJ2010A126)

摘　　要：本文讨论了G-morphic环与单位π-正则环的关系,并证明了(1)环R是单位π-正则环等价于对R中每个元素a,存在正整数n,使得an=e+u.并且anR∩eR=0,其中e是幂等元且u是环R中单位,(2)在约化的条件下,正则环,强正则环,强π-正则环,单位正则环,单位π-正则环与G-morphic环是等价的.The purpose of this paper is to prove some properties of the unit π- regular rings and to show some relations among G-morphic rings, unit π- regular rings and some special ones. We prove that： （1） A ring R is unit π- regular if and only if, for every element a of R, there exists n ∈ Z＋, such that aan can be written as e ＋ u, and anR∩ eR = 0, where e is an idempotent and u is a unit in R, （2） In a reduced ring, regular ring, strongly regular rings, unit ~r - regular ring and G-morphic ring are eqnivalent.

关 键 词：G-MORPHIC环 单位π-正则环 幂等元 单位 

分 类 号：O153.3[理学—数学]