Some results on a graph associated with a non-quasi-local atomic domain
Abstract
Let R be an atomic domain which admits at least two maximal ideals. Let Irr(R) denote the set of all irreducible elements of R and let A(R) = {Rπ | π ∈ Irr(R)}. Let I(R) denote the subset of A(R) consisting of all Rπ ∈ A(R) such that π does not belong to the Jacobson radical of R. With R, we associate an undirected graph denoted by G(R) whose vertex set is I(R) and distinct vertices Rπ1 and Rπ2 are adjacent if and only if Rπ1 ∩ Rπ2 = Rπ1π2. The aim of this article is to discuss some results on the connectedness of G(R) and on the girth of G(R).
Copyright (c) 2023 S. Visweswaran, T. Premkumar
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