关于J-quasipolar环（英文）  

On J-quasipolar Rings

作　　者：郑振 陈焕艮[1] ZHENG Zhen;CHEN Huanyin(School of Science, Hangzhou Normal University, Hangzhou 310030, China)

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2018年第2期191-194,202,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY17A010018)

摘　　要：2012年,崔建和陈建龙提出了J-quasipolar元的概念.对于环R中的一个元素a,如果存在p^2=p∈comm^2(a)使得a+p∈J(R),则称a为J-quasipolar的.一个环称为J-quasipolar的,如果环中每一个元素都是J-quasipolar的.文章证明了一个环R是J-quasipolar环的充分必要条件是环R是quasipolar环并且环R是强J~#-clean环.同时也证明了一个环R是nil-quasipolar环当且仅当环R是J-quasipolar环并且J(R)是幂零的.The notion of J-quasipolar elements of rings was introduced by Cui Jian and Chen Jianlong in 2012.An element a in a ring Ris J-quasipolar if there exists p^2=p∈comm^2（a）satisfying a＋p∈J（R）,A ring called J-quasipolar ring if every element is J-quasipolar.It is shown that Ris a J-quasiolar ring if and only if for Ris a quasipolar ring and Ris a strongly J~#-clean ring.It is also proved that Ris nil-quasipolar ring if and only if Ris J-quasipolar ring and J（R）is nil.

关 键 词：J-quasipolar环 JACOBSON根 布尔环 强nil-clean环 

分 类 号：O153.3[理学—数学]