拟polar环的注记(英文)  

Notes on Quasipolar Rings

作　　者：崔建[1,2] 陈建龙[1] 

机构地区：[1]东南大学数学系,江苏南京210096 [2]安徽师范大学数学系,安徽芜湖241000

出　　处：《数学研究》2012年第2期167-174,共8页Journal of Mathematical Study

基　　金：supported by Foundation item:the NSF of China(10971024);the Specialized Research Fund for the Doctoral Program of Higher Education(200802860024)

摘　　要：称一个环R中的元素a是拟polar元,若存在p2=P∈R满足p∈comm_R^2(a),a+P∈U(R)并且ap∈R^(qnil);且称环R是拟polar的如果R中每一个元素都是拟polar元.本文证明了,任一环R中强π-正则元是拟polar的,而拟polar元是强clean的.拟polar环的一些扩张性质也作了探讨.An element a in a ring R is called quasipolar if there exists p2 = p ∈ R such that p ∈comm2R（α）, a＋p E U（R） and ap E Rqnil; and a ring R is said to be quasipolax in case every element of R is quasipolar. In this note, we prove that any strongly π-regulax element in a ring R is quasipotar, and any quasipolar element in R is strongly clean. Several extension properties of quasipolar rings are also investigated.

关 键 词：拟polar环 强clean环 强π-正则环 谱幂等元 

分 类 号：O153.3[理学—数学]