摘要
设R是环,J(R)是R的Jacobson根.R的元素a称为半正则元,如果存在正则元b∈R使得a-b∈J(R).环R称为几乎半正则环,如果对R的任意元a,有a或者1-a是半正则的.本文引入了几乎半正则环作为VNL-环和半正则环的推广.构造了一些例子,证明了几乎半正则环是置换环;将半正则环的许多性质推广到了几乎半正则环上.
Let R be a ring and J（R） the Jacobson radical. An element a of R is called semiregular if there exists a regular element b ∈ R with a-b ∈ J（R）. A ring R is said to be feckly semiregular provided that any element a of R, either a or 1 - a is semiregular. We introduce, in this paper, feckly semiregular rings as the generalization of VNL-rings and semiregular rings. It is shown that feckly semiregular rings are exchange rings and many properties of semiregular rings can be extended onto feckly semiregular rings. Relative examples are also constructed.
出处
《数学进展》
CSCD
北大核心
2018年第1期56-64,共9页
Advances in Mathematics（China）
基金
supported by the Scientific Research Foundation of Hunan Provincial Education Department(No.12B101)
关键词
半正则环
几乎半正则环
扩张
semiregular ring
feckly semiregular ring
extension
