杭州师范大学学报（自然科学版）2016，Vol.15Issue(6)：623-631,9.DOI:10.3969/j.issn.1674-232X.2016.06.012
关于Pseudo Weakly J-clean环
On Pseudo Weakly J-clean Rings
摘要
Abstract
A ring R is called a pseudo weakly J‐clean ring if every element a∈ R can be written in the form of a= e+ w+ (1-e)Ra or a= -e+ w+ (1-e)Ra where e is an idempotent and w belongs to the Jacobson radical . This paper explores various properties of pseudo weakly J‐clean rings .A ring R is pseudo weakly J‐clean if and only if R[[x]] ,Hurwitz series ring H(R) ,trivial extension T(R ,M) and S(R ,σ) are pseudo weakly J‐clean , respectively .Furthermore ,it proves that the following are equivalent ,for any n∈ N ,Sn(R) is pseudo J‐clean , for any n∈N ,R[x]/(xn ) is pseudo weakly J‐clean ,where (xn ) is the ideal generated by xn .In particular ,it characterize S= R[D ,C] is pseudo weakly J‐clean under certain conditions .Also it shows that 2 is a unit in R , then R is pseudo J‐clean if and only if RC2 is pseudo J‐clean .关键词
pseudo weakly J-clean环/Hurwitz级数环/S= RD,C环/群环/Jacobson根/幂等元Key words
pseudo weakly J-clean ring/Hurwitz series ring/S=R[D,C] ring/group ring/Jacobson radi-cal/idempotent分类
数理科学引用本文复制引用
胡小美,陈焕艮..关于Pseudo Weakly J-clean环[J].杭州师范大学学报（自然科学版）,2016,15(6):623-631,9.基金项目
Supported by the Natural Science Foundation of Zhejiang Province （LY17A010018）． （）
