The principal small intersection graph of a commutative ring

• 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. 67, Nº. 1, 2024, págs. 245-256
• Idioma: inglés
• DOI: 10.33044/revuma.3486
• Enlaces
  • Texto completo
• Resumen

  • Let R be a commutative ring with non-zero identity. The small intersection graph of R, denoted by G(R), is a graph with the vertex set V(G(R)), where V(G(R) is the set of all proper non-small ideals of R and two distinct vertices I and J are adjacent if and only if I∩J is not small in R. In this paper, we introduce a certain subgraph PG(R) of G(R), called the principal small intersection graph of R. It is the subgraph of G(R) induced by the set of all proper principal non-small ideals of R. We study the diameter, the girth, the clique number, the independence number and the domination number of PG(R). Moreover, we present some results on the complement of the principal small intersection graph.

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