Visweswaran, S., Parejiya, J. (2018). A note on a graph related to the comaximal ideal graph of a commutative ring. Algebraic Structures and Their Applications, 4(1), 57-76. doi: 10.29252/asta.4.1.57

Subramanian Visweswaran; Jaydeep Parejiya. "A note on a graph related to the comaximal ideal graph of a commutative ring". Algebraic Structures and Their Applications, 4, 1, 2018, 57-76. doi: 10.29252/asta.4.1.57

Visweswaran, S., Parejiya, J. (2018). 'A note on a graph related to the comaximal ideal graph of a commutative ring', Algebraic Structures and Their Applications, 4(1), pp. 57-76. doi: 10.29252/asta.4.1.57

Visweswaran, S., Parejiya, J. A note on a graph related to the comaximal ideal graph of a commutative ring. Algebraic Structures and Their Applications, 2018; 4(1): 57-76. doi: 10.29252/asta.4.1.57

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

^{}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 I\not\subseteq J(R), where J(R) is the Jacobson radical of R and distinct vertices I_{1}, I_{2}are adjacent in \mathcal{G}(R) if and only if I_{1}∩ I_{2} = I_{1}I_{2}. 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.