杭州师范大学学报（自然科学版）2017，Vol.16Issue(3)：290-296,7.DOI:10.3969/j.issn.1674-232X.2017.03.012
关于J-clean环
On J-clean Rings
摘要
Abstract
A ring R is called a J-clean ring if every element a∈R can be written in the form of a=e+j where e is an idempotent and j belongs to the Jacobson radical.This article explores various properties of J-clean rings and Morita contexts,proves that the ring R is J-clean if and only if R is clean and R/J(R) is Boolean.The ring R is J-clean if and only if R[[x1,…,xn]],R(M),R[[x]] and R∝M are J-clean.Each J-clean ring R is right (left) quasi-duo ring.Furthermore,let R:=AMNB be a Morita context,then R is J-clean ring if and only if A,B are J-clean rings and MN(∈)J(A) and NM(∈)J(B).Let R be a ring with s∈C(R),then S=Ks(R) is J-clean if and only if R is J-clean and s∈J(R).Let R be a ring with s∈C(R),then Mn(R;s) is J-clean if and only if R is J-clean and s∈J(R).关键词
J-clean环/环的扩张/Moritacontext/Jacobson根Key words
J-clean ring/extension of rings/Morita context/Jacobson radical分类
数理科学引用本文复制引用
胡小美,陈焕艮..关于J-clean环[J].杭州师范大学学报（自然科学版）,2017,16(3):290-296,7.基金项目
Supported by the Natural Science Foundation of Zhejiang Province (LY17A010018). （LY17A010018）
