杭州师范大学学报（自然科学版）Issue(6)：616-624,9.DOI:10.3969/j.issn.1674-232X.2015.06.011
关于Weakly J-Clean环
On Weakly J-Clean Rings
摘要
Abstract
A ring R is called a weakly J‐clean ring if every element a∈ R can 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 R is weakly J‐clean if and only if R is clean and R/J(R) is weakly Boolean ,if and only if R/6R is weakly J‐clean and idempotents can lift J(R) .A ring R is uniquely weakly nil clean if and only if R is abelian;J(R) is nil and R is weakly J‐clean .Each weakly J‐clean ring R is right(left) quasi‐duo ring .Furthermore ,the paper proves that the following are equivalent :R is J‐clean;there is an integer n≥1 such that Tn (R) is J‐clean ;there is an integer n≥2 such that Tn (R) is weakly J‐clean;there is an integer n≥2 such that × n R is w eakly J‐clean .关键词
weakly J-clean环/clean环/唯一weakly nil clean环/幂等元/Jacobson根Key words
weakly J-clean ring/clean ring/uniquely weakly nil clean ring/idempotent/Jacobson radical分类
数理科学引用本文复制引用
沈洪地,陈焕艮..关于Weakly J-Clean环[J].杭州师范大学学报（自然科学版）,2015,(6):616-624,9.基金项目
Supported by the Natural Science Foundation of Zhejiang Province （LY13A010019）． （）
