Intersection graph of idealizations
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Mahmoodi, Akram
[1]
;
Vahidi, Alireza
[1]
;
Manaviyat, Raufeh
[1]
;
Alipour, Roghaieh
[1]
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[1] Payame Noor University
Payame Noor University
Irán
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 693-702
- Idioma: inglés
- DOI: 10.1007/s13348-023-00407-7
- Texto completo no disponible (Saber más ...)
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Resumen
Let R be a commutative ring with identity. The intersection graph of ideals of a ring R is an undirected simple graph denoted by whose vertices are in a one-to-one correspondence with non-zero proper ideals and two distinct vertices are joined by an edge if and only if the corresponding ideals of R have a non-zero intersection. Let M be a unitary R-module and let be the idealization of M in R. In this paper, we investigate the interplay between the algebraic properties of and the graph-theoretic properties of . Under some conditions on the ring R and the module M, we determine the exact form of ideals of and characterize all rings R and modules M for which is a star graph. Also, we give a necessary and sufficient condition under which is uniform and then we conclude that when is a complete graph. Among other results, some graph-theoretic properties of such as domination number, connectedness and grith are obtained.
