Counterexamples for some results in “On the module intersection graph of ideals of rings”

• Farideh Heydari ^[1] ; Soheila Khojasteh ^[1]
  1. [1] Islamic Azad University

     Islamic Azad University

     Irán

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 1, 2025, págs. 243-249
• Idioma: inglés
• DOI: 10.33044/revuma.3826
• Enlaces
  • Texto completo
• Resumen

  • 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 GM(R), is a graph with the vertex set I(R) ∗, and two distinct vertices I and J are adjacent if and only if IM ∩ JM ̸= 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 GM(R) and derive a necessary and sufficient condition for GM(R) to be weakly triangulated.

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