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| Ultima descărcare din IBN: 2023-10-13 12:33 |
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| 512.5+519.95 (1) |
| Алгебра (400) |
 SM ISO690:2012TALEBI, Yahya, AKBARZADEH, Sahar. Properties of annihilator graph of a commutative semigroup. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, nr. 3(88), pp. 22-31. ISSN 1024-7696. |
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 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 3(88) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| CZU: 512.5+519.95 | ||||||
| MSC 2010: 20M14, 05C75. | ||||||
| Pag. 22-31 | ||||||
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| Rezumat | ||||||
Let S be a commutative semigroup with zero. Let Z(S) be the set of all zero-divisors of S. We define the annihilator graph of S, denoted by ANNG(S), as the undirected graph whose set of vertices is Z(S) = Z(S) − {0}, and two distinct vertices x and y are adjacent if and only if annS(xy) 6= annS(x) ∩ annS(y). In this paper, we study some basic properties of ANNG(S) by means of Г(S). We also show that if Z(S) 6= S, then ANNG(S) is a subgraph of Г(S). Moreover, we investigate some properties of the annihilator graph ANNG(S) related to minimal prime ideals of S. We also study some connections between the domination numbers of annihilator graphs and zero-divisor graphs. |
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| Cuvinte-cheie Annihilator graph, diameter, girth, zero divisor graph. |
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