Abelian doppelsemigroups
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,...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Abelian doppelsemigroups / A.V. Zhuchok, K. Knauer // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 290–304. — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 doppel-semigroup, give examples of abelian doppelsemigroups and find conditions under which the operations of an abelian doppelsemi-group coincide.
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| ISSN: | 1726-3255 |