强拟诣零clean环（英文）

Strongly Quasi-nil Clean Rings

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.