Revista de la
Unión Matemática Argentina
Counterexamples for some results in “On the module intersection graph of ideals of rings”
Farideh Heydari and Soheila Khojasteh

Volume 68, no. 1 (2025), pp. 243–249    

Published online (final version): May 21, 2025

https://doi.org/10.33044/revuma.3826

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Abstract

Let $R$ be a commutative ring and $M$ be an $R$-module, and let $I(R)^*$ be the set of all nontrivial ideals of $R$. The $M$-intersection graph of ideals of $R$, denoted by $G_M(R)$, is a graph with the vertex set $I(R)^*$, and two distinct vertices $I$ and $J$ are adjacent if and only if $IM\cap JM\neq 0$. In this note, we provide counterexamples for some results proved in a paper by Asir, Kumar, and Mehdi [Rev. Un. Mat. Argentina 63 (2022), no. 1, 93–107]. Also, we determine the girth of $G_M(R)$ and derive a necessary and sufficient condition for $G_M(R)$ to be weakly triangulated.

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