杭州师范大学学报（自然科学版）2017，Vol.16Issue(2)：173-180,186,9.DOI:10.3969/j.issn.1674-232X.2017.02.010
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 for any a∈R can be written as a=e+j or a=-e+j,in which e is idempotent and jn belongs to Jacobson radical.This article proves a ring R is a weakly nil-clean ring if and only if R is weakly J#-clean ring and J(R) is nilpotent.If I is nilpotent,then R is a weakly J#-clean ring if and only if R/I is a weakly J#-clean ring.A ring R is a weakly J#-clean ring if and only if R/P(R),R×M,power series ring R[[x]] are weakly J#-clean rings respectively.Furthermore,it is proved that the followings are equivalent respectively,R is a J#-clean ring,there is an integer n≥1 such that Tn(R) is a J#-clean ring,there is an integer n≥2 such that Tn(R) is a weakly J#-clean ring.Also,R is a J#-clean ring,there is an integer n≥1 such that ×nR is a J#-clean ring,there is an integer n≥2 such that ×nR is a weakly J#-clean ring.In particular,S=R[D,C] is weakly J#-clean under certain conditions is exposed.关键词
weaklyJ#-clean环/clean环/weaklynilclean环/S=R[D,C]环/幂等元/Jacobson根Key words
weakly J#-clean ring/clean ring/weakly nil clean/S=R[D/C] ring/idempotent/Jacobson radical分类
数理科学引用本文复制引用
郝亚璞,陈焕艮..关于Weakly J#-clean环[J].杭州师范大学学报（自然科学版）,2017,16(2):173-180,186,9.基金项目
Supported by the Natural Science Foundation of Zhejiang Province (LY17A010018). （LY17A010018）
