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 ≠ 0 and 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)*. Let H(R) be the graph associated with R whose vertex set is I(R)* and distinct vertices...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2019 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188427 |
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| Cite this: | Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case / S. Visweswaran, P. Vadhel // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 117–143. — Бібліогр.: 14 назв. — англ. |
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Visweswaran, S. Vadhel, P. 2023-02-28T19:23:56Z 2023-02-28T19:23:56Z 2019 Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case / S. Visweswaran, P. Vadhel // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 117–143. — Бібліогр.: 14 назв. — англ. 1726-3255 2010 MSC: 13A15, 05C25. https://nasplib.isofts.kiev.ua/handle/123456789/188427 The rings we consider in this article are commutative with identity 1 ≠ 0 and 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)*. Let H(R) be the graph associated with R whose vertex set is I(R)* and distinct vertices I, J are adjacent if and only if IJ ≠ (0). The aim of this article is to discuss the planarity of H(R) in the case when R is quasilocal. We are very much thankful to the referee and all the members of the Editorial Board of Algebra and Discrete Mathematics for their suggestions and support. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case |
| spellingShingle |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case Visweswaran, S. Vadhel, P. |
| 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 |
| author |
Visweswaran, S. Vadhel, P. |
| author_facet |
Visweswaran, S. Vadhel, P. |
| publishDate |
2019 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
The rings we consider in this article are commutative with identity 1 ≠ 0 and 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)*. Let H(R) be the graph associated with R whose vertex set is I(R)* and distinct vertices I, J are adjacent if and only if IJ ≠ (0). The aim of this article is to discuss the planarity of H(R) in the case when R is quasilocal.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188427 |
| citation_txt |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case / S. Visweswaran, P. Vadhel // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 117–143. — Бібліогр.: 14 назв. — англ. |
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| first_indexed |
2025-12-07T15:48:28Z |
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2025-12-07T15:48:28Z |
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