与素根相关的矩阵子环CLEAN性  

Cleanness of Matrix Subrings Involving Prime Radicals

作　　者：李颉琛 陈焕艮[1] LI Jiechen;CHEN Huanyin(School of Science,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学理学院

出　　处：《杭州师范大学学报（自然科学版）》2019年第5期529-534,560,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY17A010018)

摘　　要：称环R是强P-clean的如果环R中的每一个元素都可以表示成一个幂等元与一个强幂零元之和.本文中我们研究了一些3×3矩阵环的强P-clean性.称环R为强2-P-clean的.如果环R中的每一个元素可以表示成一个tripotent元与一个强幂零元之和.我们证明了如果一个环是强2-P-clean的,当且仅当对于环R中的任意元素a有a^3-a∈P(R)以及存在环R中正交幂等元e和f使得a-e+f∈P(R).进而我们得到了强2-P-clean矩阵子环的相关结论.A ring R is strongly P-clean if every element in R is the sum of an idempotent and a strong nilpotent.In this paper,the strong P-cleanness of certain 3×3 matrix rings is investigated.A ring R is strongly 2-P-clean if every element in R is the sum of a tripotent and a strong nilpotent.Elementary results on such rings are derived.It is proved that a ring R is strongly 2-P-clean if and only if for any a∈R,a^3-a∈P(R)if and only if for any a∈R,there exist orthogonal idempotents e,f∈R such that a-e+f∈P(R).Furthermore,the related results about on strongly 2-P-clean matrix subrings are obtained as well.

关 键 词：强P-clean环 强2-P-clean环 tripotent 2-primal环 

分 类 号：O153.3[理学—数学] E50[理学—基础数学]