Some results on a supergraph of the comaximal ideal graph of a commutative ring

Document Type: Original paper

Authors

1 Saurashtra University

2 Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India.

Abstract

Let R be a commutative ring with identity such that R admits at least two maximal ideals. In this article, we associate a graph with R whose vertex set is the set of all proper ideals I of R such that I is not contained in the Jacobson radical of R and distinct vertices I and J are joined by an edge if and only if I and J are not comparable under the inclusion relation. The aim of this article is to study the interplay between the graph-theoretic properties of this graph and the ring-theoretic properties of the ring R.

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