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.
Publisher
University of Baghdad College of Science
Subject
General Biochemistry, Genetics and Molecular Biology,General Chemistry,General Computer Science
Cited by
2 articles.
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1. Maximal submodule graph of a module;Journal of Discrete Mathematical Sciences and Cryptography;2021-10-03
2. Analysing the structure of A4-graphs for Mathieu groups;Journal of Discrete Mathematical Sciences and Cryptography;2021-10-03