Manal Al-Labadi, "When Intersection Ideals of Graphs of Rings are a Divisor graph," WSEAS Transactions on Mathematics, vol. 19, pp. 430-434, 2020, DOI:10.37394/23206.2020.19.44
Manal Al-Labadi. When Intersection Ideals of Graphs of Rings are a Divisor graph.
WSEAS Transactions on Mathematics. 2020;19:430-434. 10.37394/23206.2020.19.44
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
When Intersection Ideals of Graphs of Rings are a Divisor graph
Author:
Abstract: Let R be a commutative principal ideal ring with unity. In this paper, we classify when the intersectiongraphs of ideals of a ring R G(R), is a divisor graph. We prove that the intersection graphs of ideals of a ring RG(R), is a divisor graph if and only if R is a local ring or it is a product of two local rings with each of them hasone chain of ideals. We also prove that G(R), is a divisor graph if it is a product of two local rings one of themhas at most two non-trivial ideals with empty intersection.
Keywords:
The commutative ring, The intersection ideals of graphs of rings R, Principal ideal ring, Local ring, Divisor graph.
Pages: 430-434 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #44 DOI: 10.37394/23206.2020.19.44
×
Citation Tools