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Algebra and Discrete Mathematics, 2019, Volume 27, Issue 1, Pages 117–143 (Mi adm697)  

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
References:
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
Document Type: Article
MSC: 13A15, 05C25
Language: English
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
Citation in format AMSBIB
\Bibitem{VadVis19}
\by P.~Vadhel, S.~Visweswaran
\paper Planarity of a spanning subgraph of~the~intersection graph of ideals of~a~commutative ring~II, Quasilocal Case
\jour Algebra Discrete Math.
\yr 2019
\vol 27
\issue 1
\pages 117--143
\mathnet{http://mi.mathnet.ru/adm697}
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