Medium诣零*-clean环  

Medium nil *-clean rings

作　　者：张习习 吴俊 ZHANG Xixi;WU Jun(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241003,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《南通大学学报（自然科学版）》2022年第1期82-87,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：安徽省高校自然科学重点基金项目(KJ2019A0488)。

摘　　要：若R是*-环,R中每个元素都可以表示成幂零元与投射元的和或者差且二者可交换,则称R是medium诣零*-clean环。文章得到了此环的基本性质,证明了*-环R是medium诣零*-clean环当且仅当R是强*-clean且是弱诣零-clean的,当且仅当R是阿贝尔弱诣零*-clean的,当且仅当R是medium*-clean且J(R)是诣零的。此外,还研究了medium诣零*-clean同态像的基本性质并得到一些等价刻画。A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of a nilpotent with a projection that commute. Fundamenta properties of such *-rings are obtained. It is proved that a *-rings R is medium nil *-clean if and only if R is strongly *-clean and weakly nil clean, while the latter holds true if and only if R is abelian and weakly nil *-clean, if and only if R is medium *-clean and J(R) is nil. Furthermore, some baisc properties of homomorphic images of such ring are explored and some equivalent characterizations are obtained.

关 键 词：medium诣零*-clean环 弱诣零*-clean环 *-clean环 

分 类 号：O153.3[理学—数学]