The small intersection graph relative to multiplication modules

Author(s):

H. Ansari , Toroghy * , F. Farshadifar , F. Mahboobi , Abkenar

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 N∩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 Mis a multiplication module.
Keywords:

Graph , non , small submodule , multiplication module

Language:
English
Published:
Journal of Algebra and Related Topics, Volume:4 Issue: 1, Summer 2016
Pages:
21 to 32
https://www.magiran.com/p1616303