强Quasinil Quasi-clean环和Quasi-polar环  

Strongly Quasinil Quasi-clean Rings and Quasi-polar Rings

作　　者：尹闯 胡傲 唐高华 YIN Chuang;HU Ao;TANG Gaohua(School of Sciences,Beibu Gulf University,Qinzhou Guangxi 535011,China)

机构地区：[1]北部湾大学理学院,广西钦州535011

出　　处：《广西师范大学学报（自然科学版）》2023年第2期118-123,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12261001,11961050);广西自然科学基金(2021GXNSFAA220043)。

摘　　要：设R是一个环,称环R的元素e为拟幂等元,如果存在R的某个中心单位k,使得e 2=ke。若R中的每个元素都存在拟幂等元e∈R,q∈R qnil使得e∈comm 2(a),并且a=e+q,则称环R是强quasinil quasi-clean环。若环R中每个元素a都存在一个拟幂等元e∈R使得e∈comm 2(a),a+e∈U(R)且ae∈R qnil,则称R是拟quasi-polar环。本文首先证明拟quasi-polar环与quasi-polar环等价,在此基础上进一步证明强nil quasi-clean环是强quasinil quasi-clean环,强quasinil quasi-clean环是quasi-polar环,但反之均不成立。Let R be a ring.An elemente in R is called a quasi-idempotent if there is a central unit k of R such that e 2=ke.If for every element a of R,there exists a quasi-idempotent e∈R and a quasinilpotent q∈R qnil such that e∈comm 2(a)and a=e+q,then R is called a strongly quasinil quasi-clean ring.If for every element a of R,there exists a quasi-idempotent e∈R such that e∈comm 2(a),a+e∈U(R)and ae∈R qnil,then R is called a quasi-quasi-polar ring.In this paper,it is proved that the quasi-quasi-polar ring and quasi-polar ring are equivalent;every strongly nil quasi-clean ring is a strongly quasinil quasi-clean ring;and every strongly quasinil quasi-clean ring is a quasi-polar ring.The inverses are not hold.

关 键 词：拟幂等元 强quasinil clean环 拟quasi-polar环 强quasinil quasi-clean环 quasi-polar环 

分 类 号：O153.3[理学—数学]