On the comaximal graph of a non-quasi-local atomic domain

Document Type : Original paper

Authors

1 Saurashtra University

2 Department of Mathematics, Dr. Subhash University, Dr. Subhash Road, Junagadh, India.

Abstract

Let $R$ be an atomic domain such that $R$ has at least two maximal ideals. Let $Irr(R)$ denote the set of all irreducible elements of $R$ and let $J(R)$ denote the Jacobson radical of $R$.  Let $\mathcal{I}(R) = \{R\pi\mid \pi\in Irr(R)\backslash J(R)\}$. In this paper,  with $R$, we associate an undirected  graph denoted by $\mathbb{CGI}(R)$  whose vertex set is $\mathcal{I}(R)$ and distinct vertices $R\pi_{1}$ and  $R\pi_{2}$ are adjacent if and only if $R\pi_{1} + R\pi_{2} = R$.  The aim of this paper is to study the interplay between some graph properties of $\mathbb{CGI}(R)$ and the algebraic properties of $R$. 

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 25 April 2024

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