Maximal Ideal Graph of Commutative Rings

F. H.  Abdulqadr

doi:10.24996/ijs.2020.61.8.22

Authors

F. H. Abdulqadr Department of Mathematics, College of Education, University of Salahaddin, Erbil, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.8.22

Keywords:

The maximal ideal graph of a commutative ring R, maximal ideals, connected graphs

Abstract

In this paper, we introduce and study the notion of the maximal ideal graph of a commutative ring with identity. Let R be a commutative ring with identity. The maximal ideal graph of R, denoted by MG(R), is the undirected graph with vertex set, the set of non-trivial ideals of R, where two vertices I₁ and I₂ are adjacent if I₁ I₂ and I₁+I₂ is a maximal ideal of R. We explore some of the properties and characterizations of the graph.