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Algebra and Discrete Mathematics, 2019, Volume 27, Issue 1, Pages 117–143
(Mi adm697)
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RESEARCH ARTICLE
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case
P. Vadhel, S. Visweswaran Department of Mathematics, Saurashtra University, Rajkot, 360 005 India
Abstract:
The rings we consider in this article are commutative with identity $1\neq 0$ and are not fields. Let $R$ be a ring. We denote the collection of all proper ideals of $R$ by $\mathbb{I}(R)$ and the collection $\mathbb{I}(R)\setminus \{(0)\}$ by $\mathbb{I}(R)^{*}$. Let $H(R)$ be the graph associated with $R$ whose vertex set is $\mathbb{I}(R)^{*}$ and distinct vertices $I, J$ are adjacent if and only if $IJ\neq (0)$. The aim of this article is to discuss the planarity of $H(R)$ in the case when $R$ is quasilocal.
Keywords:
quasilocal ring, local Artinian ring, special principal ideal ring, planar graph.
Received: 22.09.2015 Revised: 24.08.2018
Citation:
P. Vadhel, S. Visweswaran, “Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case”, Algebra Discrete Math., 27:1 (2019), 117–143
Linking options:
https://www.mathnet.ru/eng/adm697 https://www.mathnet.ru/eng/adm/v27/i1/p117
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Abstract page: | 61 | Full-text PDF : | 35 | References: | 19 |
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