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Algebra and Discrete Mathematics, 2017, том 24, выпуск 2, страницы 191–208
(Mi adm627)
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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
RESEARCH ARTICLE
On the genus of the annihilator graph of a commutative ring
T. Tamizh Chelvam, K. Selvakumar Department of Mathematics, Manonmaniam Sundaranar University,
Tirunelveli 627012, Tamil Nadu, India
Аннотация:
Let $R$ be a commutative ring and $Z(R)^*$ be its set of non-zero zero-divisors. The annihilator graph of a commutative ring $R$ is the simple undirected graph $\operatorname{AG}(R)$ with vertices $Z(R)^*$, and two distinct vertices $x$ and $y$ are adjacent if and only if $\operatorname{ann}(xy)\neq \operatorname{ann}(x)\cup \operatorname{ann}(y)$. The notion of annihilator graph has been introduced and studied by A. Badawi [7]. In this paper, we determine isomorphism classes of finite commutative rings with identity whose $\operatorname{AG}(R)$ has genus less or equal to one.
Ключевые слова:
commutative ring, annihilator graph, genus, planar, local rings.
Поступила в редакцию: 06.10.2015 Исправленный вариант: 17.07.2016
Образец цитирования:
T. Tamizh Chelvam, K. Selvakumar, “On the genus of the annihilator graph of a commutative ring”, Algebra Discrete Math., 24:2 (2017), 191–208
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm627 https://www.mathnet.ru/rus/adm/v24/i2/p191
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Страница аннотации: | 216 | PDF полного текста: | 140 | Список литературы: | 22 |
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