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Algebra Discrete Math., 2018, Volume 26, Issue 2, Pages 290–304 (Mi adm685)  

RESEARCH ARTICLE

Abelian doppelsemigroups

Anatolii V. Zhuchoka, Kolja Knauerb

a Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol square, 1, Starobilsk, 92703, Ukraine
b Laboratory of Computer Science and Systems, Aix-Marseille University, LIS UMR 7020, Case Courrier 901, 163, avenue de Luminy 13288, Marseille Cedex 9, France

Abstract: A doppelsemigroup is an algebraic system consisting of a set with two binary associative operations satisfying certain identities. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as doppelalgebras, duplexes, interassociative semigroups, restrictive bisemigroups, dimonoids and trioids. This paper is devoted to the study of abelian doppelsemigroups. We show that every abelian doppelsemigroup can be constructed from a left and right commutative semigroup and describe the free abelian doppelsemigroup. We also characterize the least abelian congruence on the free doppelsemigroup, give examples of abelian doppelsemigroups and find conditions under which the operations of an abelian doppelsemigroup coincide.

Keywords: doppelsemigroup, abelian doppelsemigroup, free abelian doppelsemigroup, free doppelsemigroup, interassociativity, semigroup, congruence, doppelalgebra.

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MSC: 08B20, 20M10, 20M50, 17A30
Received: 07.09.2018
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Citation: Anatolii V. Zhuchok, Kolja Knauer, “Abelian doppelsemigroups”, Algebra Discrete Math., 26:2 (2018), 290–304

Citation in format AMSBIB
\Bibitem{ZhuKna18}
\by Anatolii~V.~Zhuchok, Kolja~Knauer
\paper Abelian doppelsemigroups
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 2
\pages 290--304
\mathnet{http://mi.mathnet.ru/adm685}


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