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 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 |