Q-m-clean环及其推广  

Q-m-clean Rings and its Generalization

作　　者：李莹 殷晓斌 LI Ying;YIN Xiao-bin(College of Mathematics and Statistics,Anhui Normal University,Wuhu 241000,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2022年第1期18-22,共5页Journal of Anhui Normal University(Natural Science)

基　　金：安徽省自然科学基金项目(2008085MA06).

摘　　要：主要利用拟可逆元和m-potent元的概念,定义了Q-m-clean元和Q-m-clean环,给出了Q-m-clean元的一些等价条件,研究了Q-m-clean环的一些性质,证明了Q-m-clean环的同态像及有限直积均是Q-m-clean环。The concepts of Q-m-clean elements and Q-m-clean rings are defined by means of quasi-invertible elements and m-potent elements.Some equivalence conditions about Q-m-clean elements are given,some proporties about Q-m-clean rings are studied,and the relation between Q-m-clean rings and other rings are also explained.It is mainly found that the homomorphism of Q-m-clean rings are also Q-m-clean,and the finite direct product of Q-m-clean rings are also Q-m-clean.

关 键 词：Q-m-clean环 拟可逆元 ABEL环 

分 类 号：O153.3[理学—数学]