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...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2018
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188380 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712009220423680 |
|---|---|
| author | Vadhel, P. Visweswaran, S. |
| author_facet | Vadhel, P. Visweswaran, S. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T17:34:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188380 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:34:08Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case Vadhel, P. Visweswaran, S. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188380 |
| work_keys_str_mv | AT vadhelp planarityofaspanningsubgraphoftheintersectiongraphofidealsofacommutativeringinonquasilocalcase AT visweswarans planarityofaspanningsubgraphoftheintersectiongraphofidealsofacommutativeringinonquasilocalcase |