On the module intersection graph of ideals of rings

• Thangaraj Asir ^[1] ; Arun Kumar ^[2] ; Alveera Mehdi ^[2]
  1. [1] Madurai Kamaraj University

     Madurai Kamaraj University

     India

     
  2. [2] Aligarh Muslim University

     Aligarh Muslim University

     India

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 63, Nº. 1, 2022, págs. 93-107
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let R be a commutative ring and M an R-module. The M-intersection graph of ideals of R is an undirected simple graph, denoted by GM(R), whose vertices are non-zero proper ideals of R and two distinct vertices are adjacent if and only if IM ∩ JM 6= 0. In this article, we focus on how certain graph theoretic parameters of GM(R) depend on the properties of both R and M. Specifically, we derive a necessary and sufficient condition for R and M such that the M-intersection graph GM(R) is either connected or complete.

    Also, we classify all R-modules according to the diameter value of GM(R).

    Further, we characterize rings R for which GM(R) is perfect or Hamiltonian or pancyclic or planar. Moreover, we show that the graph GM(R) is weakly perfect and cograph.