VNL-环与$PP$-环的推广

A Generalization of VNL-Rings and $PP$-Rings

中文关键词:  VNL-环  左$PP$-环  左几乎$PP$-环

英文关键词:VNL-rings  left $PP$-rings  left almost $PP$-rings

中文摘要:

      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.

英文摘要:

      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.