摘要
一个环R叫做weakly J-clean环,如果R中的每一个元素都可以写成a=e+j或a=-e+j的形式,其中e是幂等元,j属于Jacobson根.文章探究了weakly J-clean环的各种性质,证明了R是weakly J-clean环当且仅当R是clean环并且R/J(R)是弱布尔环,当且仅当R/6R是weakly J-clean环且幂等元关于J(R)可以提升.一个环R是唯一weakly nil clean环当且仅当R是阿贝尔环;J(R)是幂零的并且R是weakly J-clean环.每个weakly J-clean环R是右(左)quasi-duo环.并进一步证明以下几点是等价的:R是J-clean环;存在一个大于等于1的整数n,使得Tn(R)是J-clean环;存在一个大于等于2的整数n,使得Tn(R)是weakly J-clean环;存在一个大于等于2的整数n,使得×nR是weakly J-clean环.
A ring Ris called a weakly J-clean ring if every element a∈Rcan be written in the form of a=e＋j or a=-e＋j where e is an idempotent and j belongs to the Jacobson radical.The paper explores various properties of weakly J-clean rings,proves that a ring Ris weakly J-clean if and only if Ris clean and R/J（R）is weakly Boolean,if and only if R/6Ris weakly J-clean and idempotents can lift J（R）.A ring Ris uniquely weakly nil clean if and only if Ris abelian;J（R）is nil and Ris weakly J-clean.Each weakly J-clean ring Ris right（left）quasi-duo ring.Furthermore,the paper proves that the following are equivalent：Ris J-clean;there is an integer n≥1such that Tn（R）is J-clean;there is an integer n≥2such that Tn（R）is weakly J-clean;there is an integer n≥2such that×nRis weakly J-clean.
出处
《杭州师范大学学报（自然科学版）》
CAS
2015年第6期616-624,共9页
Journal of Hangzhou Normal University(Natural Science Edition)
基金
Supported by the Natural Science Foundation of Zhejiang Province(LY13A010019)
