| VNL-环与$PP$-环的推广 |
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| 引用本文： | 向跃明. VNL-环与$PP$-环的推广[J]. 数学研究及应用, 2017, 37(2): 199-209 |
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| 作者姓名： | 向跃明 |
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| 作者单位： | 怀化学院数学与应用数学系, 湖南 怀化 418000 |
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| 基金项目： | 湖南省自然科学基金(Grant No.2016JJ2050). |
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| 摘 要： | 设$R$是环. $R$的一个元素$a$称为左$PP$-元,如果$Ra$是投射的. 环$R$称为左几乎$PP$-环,如果对$R$的任意元素$a$, $a$或者$1-a$是左$PP$-元. 本文中我们引入了左几乎$PP$-环作为VNL-环和左$PP$-环的推广. 我们构造了一些例子研究了左几乎$PP$-环的一些性质.
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| 关 键 词： | VNL-环 左$PP$-环 左几乎$PP$-环 |
| 收稿时间： | 2016-01-05 |
| 修稿时间： | 2016-11-23 |
A Generalization of VNL-Rings and $PP$-Rings |
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| Yueming XIANG. A Generalization of VNL-Rings and $PP$-Rings[J]. Journal of Mathematical Research with Applications, 2017, 37(2): 199-209 |
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| Authors: | Yueming XIANG |
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| Affiliation: | Department of Mathematics and Applied Mathematics, Huaihua University, Hunan 418000, P. R. China |
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| Abstract: | Let $R$ be a ring. An element $a$ of $R$ is called a left $PP$-element if $Ra$ is projective. The ring $R$ is said to be a left almost $PP$-ring provided that for any element $a$ of $R$, either $a$ or $1-a$ is left $PP$. We develop, in this paper, left almost $PP$-rings as a generalization of von Neumann local (VNL) rings and left $PP$-rings. Some properties of left almost $PP$-rings are studied and some examples are also constructed. |
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| Keywords: | VNL-rings left $PP$-rings left almost $PP$-rings |
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