The small intersection graph relative to multiplication modules

Document Type : Research Paper

Authors

¹ University of Guilan

² University of Farhangian

Abstract

Let

R

be a commutative ring and let

M

be an

R

-module. We define the small intersection graph

G (M)

M

with all non-small proper submodules of

M

as vertices and two distinct vertices

N, K

are adjacent if and only if

N \cap 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.

Keywords