J-clean环的推广  

Generalizations of J-clean Rings

作　　者：崔建 秦龙 CUI Jian;QIN Long(Department of Mathematics,Anhui Normal University,Wuhu,Anhui,241002,P.R.China)

机构地区：[1]安徽师范大学数学系,芜湖安徽241002

出　　处：《数学进展》2020年第1期29-38,共10页Advances in Mathematics（China）

基　　金：This research is supported by NSFC(No.11401009);A nhui Provincial Natural Science Foundation(No.1408085QA01).

摘　　要：如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环.A ring R is J-clean(respectively,UJ) if every element(respectively,unit) of R is a sum of an idempotent and an element from the Jacobson radical of R.All J-clean rings are UJ rings.In this paper,we introduce the notion of a GUJ ring,which is a proper generalization of UJ rings.The properties and applications of GUJ rings are discussed.We also investigate rings for which every element is a sum of an idempotent and an element whose power belongs to the Jacobson radical.

关 键 词：CLEAN环 J-clean环 UJ环 诣零clean环 GJ-clean环 

分 类 号：O153.3[理学—数学]