强拟诣零clean环（英文）  

Strongly Quasi-nil Clean Rings

作　　者：汪慧星 WA.NG Huixing(School of Mathematics and Statistics;Anhui Normal University,Wuhu,Anhui,241003,P.R.China)

机构地区：[1]安徽师范大学数学与统计学院,芜湖安徽241003

出　　处：《数学进展》2019年第1期53-60,共8页Advances in Mathematics（China）

基　　金：Supported in part by NSFC(No.11401009);Anhui Provincial Natural Science Foundation(No.1408085QA01);the Key Natural Science Foundation of Anhui Educational Committee(No.KJ2014A082)

摘　　要：环R中元素a称为强拟诣零clean元,若存在幂等元e∈R和拟幂零元q∈R使得eq=qe且a=e+q;称环R为强拟诣零clean环,如果R中每一个元素均是强拟诣零clean元.强拟诣零clean环介于强诣零clean环和强clean环之间,并且每一个强拟诣零clean元是强clean元.本文介绍了强拟诣零clean环的基本性质和结构,并研究了局部环R上广义矩阵环K_s(R)的强拟诣零clean性.An element a of a ring R is called strongly quasi-nil clean if there exist e^2=e€R and q€2Zqn11 satisfying eq=qe and a=e+g;R is called strongly quasi-nil clean in case each of its elements is strongly quasi-nil clean.The class of this sort of rings lies properly between the classes of strongly nil clean rings and strongly clean rings.In particular,every strongly quasi-nil clean element in a ring is strongly clean.In this paper,some basic properties and structures of strongly quasirnil clean rings are shown.Moreover,strongly quasi-nil cleanness of generalized matrix rings Ks(R)over a local ring R is investigated.

关 键 词：强拟诣零clean环 局部环 广义矩阵环 

分 类 号：O153.3[理学—数学]