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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2015, Volume 20, Issue 1, Pages 32–39 (Mi adm529)

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.

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Bibliographic databases:
MSC: 20M
Revised: 07.09.2015
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Citation: Vitaliy M. Bondarenko, Yaroslav V. Zaciha, “On characteristic properties of semigroups”, Algebra Discrete Math., 20:1 (2015), 32–39

Citation in format AMSBIB
\Bibitem{BonZac15} \by Vitaliy~M.~Bondarenko, Yaroslav~V.~Zaciha \paper On characteristic properties of semigroups \jour Algebra Discrete Math. \yr 2015 \vol 20 \issue 1 \pages 32--39 \mathnet{http://mi.mathnet.ru/adm529} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431949} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700004}