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数学进展 - 2018, Vol. 47(1): 56-64
研究论文
几乎半正则环
Feckly Semiregular Rings

向跃明
XIANG Yueming

怀化学院数学与应用数学系, 怀化, 湖南, 418000
Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua, Hunan, 418000, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 56-64
DOI: 10.11845/sxjz.2016038b


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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 $b\in R$ 使得 $a-b\in J(R)$.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${\rm VNL}$-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.
关键词 半正则环几乎半正则环扩张    
Abstract: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 $b\in R$ with $a-b\in J(R)$.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.
Key wordssemiregular ring    feckly semiregular ring    extension
PACS:  O153.3  
通讯作者: E-mail: xymls999@126.com   
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