关于J-clean环（英文）  

On J-clean Rings

作　　者：胡小美[1] 陈焕艮[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2017年第3期290-296,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY17A010018)

摘　　要：一个环R叫做J-clean环,如果R中的每一个元素都可以写成a=e+j的形式,其中e是幂等元,j属于Jacobson根,文章探究了J-clean环的各种性质和Morita contexts,证明了环R是J-clean当且仅当R是clean环和R/J(R)是布尔环;环R是J-clean当且仅当R[[x_1,…,x_n]],R(M),R[[x]]和R∝M是J-clean,每个J-clean环R是右(左)quasi-duo环.更多的,当R:=(A M/N B)是一个Morita context,则R是J-clean环当且仅当A,B是J-clean环并且MN■J(A)和NM■J(B);当R是一个环且s∈C(R),则S=K_s(R)是J-clean当且仅当R是J-clean且s∈J(R);当R是一个环且s∈C(R),则M_n(R;s)是J-clean当且仅当R是J-clean和s∈J(R).A ring R is called a J-clean ring if every element a E 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 RccM are J-clean. Each J-clean ring R is right （left） quasi-duo ring. Furthermore, let R： =（A M N B） be a Morita context, then R is J-clean ring if and only if A, B N B are J-clean rings and MN J（A） and NM J（B）. Let R be a ring with s∈C（R）, then S=K,（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 MORITA CONTEXT JACOBSON根 

分 类 号：O153.3[理学—数学]