Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case
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 gra...
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| Дата: | 2019 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2019
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-392019-03-23T17:44:10Z Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case Visweswaran, S. Vadhel, P. quasilocal ring, local Artinian ring, special principal ideal ring, planar graphPlanar graph, Clique number of a graph, Quasilocal ring, Special principal ideal ring 13A15, 05C25 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. Lugansk National Taras Shevchenko University 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/39 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/39/pdf Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
quasilocal ring local Artinian ring special principal ideal ring planar graphPlanar graph Clique number of a graph Quasilocal ring Special principal ideal ring 13A15 05C25 |
| spellingShingle |
quasilocal ring local Artinian ring special principal ideal ring planar graphPlanar graph Clique number of a graph Quasilocal ring Special principal ideal ring 13A15 05C25 Visweswaran, S. Vadhel, P. Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| topic_facet |
quasilocal ring local Artinian ring special principal ideal ring planar graphPlanar graph Clique number of a graph Quasilocal ring Special principal ideal ring 13A15 05C25 |
| format |
Article |
| author |
Visweswaran, S. Vadhel, P. |
| author_facet |
Visweswaran, S. Vadhel, P. |
| author_sort |
Visweswaran, S. |
| title |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| title_short |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| title_full |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| title_fullStr |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| title_full_unstemmed |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| title_sort |
planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring ii, quasilocal case |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/39 |
| work_keys_str_mv |
AT visweswarans planarityofaspanningsubgraphoftheintersectiongraphofidealsofacommutativeringiiquasilocalcase AT vadhelp planarityofaspanningsubgraphoftheintersectiongraphofidealsofacommutativeringiiquasilocalcase |
| first_indexed |
2024-04-12T06:25:17Z |
| last_indexed |
2024-04-12T06:25:17Z |
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