Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case
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 g...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2018
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| Zitieren: | 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, № 1. — С. 130–143. — Бібліогр.: 19 назв. — англ. |
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Vadhel, P. Visweswaran, S. 2023-02-26T12:36:01Z 2023-02-26T12:36:01Z 2018 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, № 1. — С. 130–143. — Бібліогр.: 19 назв. — англ. 1726-3255 2010 MSC: 13A15, 05C25. https://nasplib.isofts.kiev.ua/handle/123456789/188380 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). 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 ≠ (0). The purpose of this article is to characterize rings R with at least two maximal ideals such that H(R) is planar. 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 I, nonquasilocal case Article published earlier |
| institution |
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 I, nonquasilocal case |
| spellingShingle |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case Vadhel, P. Visweswaran, S. |
| title_short |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case |
| title_full |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case |
| title_fullStr |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case |
| title_full_unstemmed |
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case |
| title_sort |
planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring i, nonquasilocal case |
| author |
Vadhel, P. Visweswaran, S. |
| author_facet |
Vadhel, P. Visweswaran, S. |
| publishDate |
2018 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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). 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 ≠ (0). The purpose of this article is to characterize rings R with at least two maximal ideals such that H(R) is planar.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188380 |
| citation_txt |
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, № 1. — С. 130–143. — Бібліогр.: 19 назв. — англ. |
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2025-12-07T17:34:08Z |
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