A generalization of supplemented modules

Details A generalization of supplemented modules A generalization of supplemented modules

2011-08-17

arxiv.org/abs/1108.3381v1

Mathematics

Rings and Algebras

14

Scientific paper

Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is called an $I$-supplemented module (finitely $I$-supplemented module) if for every submodule (finitely generated submodule) $X$ of $M$, there is a submodule $Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in $Y$. This definition generalizes supplemented modules and $\delta$-supplemented modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some well known results are obtained as corollaries.

Affiliated with

Also associated with

No associations

Rating

A generalization of supplemented modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A generalization of supplemented modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generalization of supplemented modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539648