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Algebra and Discrete Mathematics, 2015, Volume 20, Issue 1, Pages 32–39
(Mi adm529)
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RESEARCH ARTICLE
On characteristic properties of semigroups
Vitaliy M. Bondarenko, Yaroslav V. Zaciha Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev
Abstract:
Let $\mathcal{K}$ be a class of semigroups and $\mathcal{P}$ be a set of general properties of semigroups. We call a subset $Q$ of $\mathcal{P}$ characteristic for a semigroup $S\in\mathcal{K}$ if, up to isomorphism and anti-isomorphism, $S$ is the only semigroup in $\mathcal{K}$, which satisfies all the properties from $Q$.
The set of properties $\mathcal{P}$ is called char-complete for $\mathcal{K}$ if for any $S\in \mathcal{K}$
the set of all properties $P\in\mathcal{P}$, which hold for the semigroup $S$, is characteristic for $S$. We indicate a 7-element set of properties of semigroups which is a minimal char-complete set for the class of semigroups of order $3$.
Keywords:
semigroup, anti-isomorphism, idempotent, Cayley table, characteristic property, char-complete set.
Received: 07.09.2015 Revised: 07.09.2015
Citation:
Vitaliy M. Bondarenko, Yaroslav V. Zaciha, “On characteristic properties of semigroups”, Algebra Discrete Math., 20:1 (2015), 32–39
Linking options:
https://www.mathnet.ru/eng/adm529 https://www.mathnet.ru/eng/adm/v20/i1/p32
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Abstract page: | 181 | Full-text PDF : | 73 | References: | 42 |
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