The large sum graph related to comultiplication modules

TL;DR

This paper introduces the large sum graph for modules over commutative rings, exploring how its properties relate to the algebraic structure of comultiplication modules.

Contribution

It defines the large sum graph for modules and investigates its properties specifically for comultiplication modules, linking graph theory with module theory.

Findings

Characterization of the large sum graph for comultiplication modules

Connections between graph properties and algebraic properties of modules

Insights into the structure of non-large submodules

Abstract

Let R be a commutative ring and M be an R-module. We define the large sum graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large submodules of M and two distinct vertices are adjacent if and only if N + K is a non-large submodule of M. In this article, we investigate the connection between the graph-theoretic properties of \acute{G}(M) and some algebraic properties of M when M is a comultiplication R-module.