A Generalization of VNL-Rings and $PP$-Rings |
Received:January 05, 2016 Revised:November 23, 2016 |
Key Words:
VNL-rings left $PP$-rings left almost $PP$-rings
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Fund Project:Supported by the Natural Science Foundation of Hunan Province (Grant No.2016JJ2050). |
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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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2017.02.008 |
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