Abstract
The rings considered in this article are commutative with identity which admit at least two maximal ideals. This article is inspired by the work done on the comaximal ideal graph of a commutative ring. Let R be a ring. We associate an undirected graph to R denoted by mathcal{G}(R), whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R), where J(R) is the Jacobson radical of R and distinct vertices I1, I2are adjacent in mathcal{G}(R) if and only if I1∩ I2 = I1I2. The aim of this article is to study the interplay between the graph-theoretic properties of mathcal{G}(R) and the ring-theoretic properties of R.
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