Maximal Ideal Graph of Commutative Rings

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

Published
2020-08-28
How to Cite
Abdulqadr, F. H. (2020). Maximal Ideal Graph of Commutative Rings. Iraqi Journal of Science, 61(8), 2070-2076. https://doi.org/10.24996/ijs.2020.61.8.22
Section
Mathematics