Sum-Essential Graphs of Modules

Abstract

The sum-essential graph ${\mathcal{S}}_R(M)$ of a left $R$-module $M$ is a graph whose vertices are all nontrivial submodules of $M$ and two distinct submodules are adjacent iff their sum is an essential submodule of $M$. Properties of the graph ${\mathcal{S}}_R(M)$ and its subgraph ${\mathcal{P}}_R(M)$ induced by vertices which are not essential as submodules of $M$ are investigated. The interplay between module properties of $M$ and properties of those graphs is studied.

To appear in J. Algebra Appl