A Generalization of VNL-Rings and $PP$-Rings
Received:January 05, 2016  Revised:November 23, 2016
Key Word: VNL-rings   left $PP$-rings   left almost $PP$-rings  
Fund ProjectL:Supported by the Natural Science Foundation of Hunan Province (Grant No.2016JJ2050).
Author NameAffiliation
Yueming XIANG Department of Mathematics and Applied Mathematics, Huaihua University, Hunan 418000, P. R. China 
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      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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