The small intersection graph relative to multiplication modules

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Abstract:

Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M$, where $M$ is a multiplication module.

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Journal title

volume 4  issue 1

pages  21- 32

publication date 2016-06-01

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