A note on a graph related to the comaximal ideal graph of a commutative ring

Authors

Jaydeep Parejiya Department of Mathematics, Saurashtra University, Rajkot, India.

Subramanian Visweswaran Department of Mathematics, Saurashtra University, Rajkot, India.

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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