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Title: | Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case |
Authors: | Vadhel, P. Visweswaran, S. |
Keywords: | quasilocal ring special principal ideal ring clique number of a graph planar graph |
Issue Date: | 2018 |
Publisher: | ДЗ "ЛНУ імені Тараса Шевченка" |
Series/Report no.: | математичні науки; |
Abstract: | The rings considered in this article are nonzero commutative with identity which are not fields. Let R be a ring. We denote the collection of all proper ideals of R by I(R) and the collection I(R)\{(0)} by I(R) ∗ . Recall that the intersection graph of ideals of R, denoted by G(R), is an undirected graph whose vertex set is I(R) ∗ and distinct vertices I, J are adjacent if and only if I ∩J = (0) 6 . In this article, we consider a subgraph of G(R), denoted by H(R), whose vertex set is I(R) ∗ and distinct vertices I, J are adjacent in H(R) if and only if IJ 6= (0). The purpose of this article is to characterize rings R with at least two maximal ideals such that H(R) is planar. |
Description: | Vadhel P. Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case / P. Vadhel , S. Visweswaran // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp.130-143 |
URI: | http://hdl.handle.net/123456789/4545 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (26). - 2018 |
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