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Title: | Abelian doppelsemigroups |
Authors: | Zhuchok, A.V. Knauer, K. |
Keywords: | doppelsemigroup abelian doppelsemigroup free abelian doppelsemigroup free doppelsemigroup interassociativity semigroup congruence doppelalgebra |
Issue Date: | 2018 |
Publisher: | ДЗ"ЛНУ імені Тараса Шевченко" |
Series/Report no.: | Математичні науки; |
Abstract: | A doppelsemigroup is an algebraic system consisting of a set with two binary associative operations satisfying certain identities. Doppelsemigroups are a generalization of semi-groups 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. |
Description: | Zhuchok A.V. Abelian doppelsemigroups / A.V.Zhuchok, K.Knauer // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 2. - Рp.290-304 |
URI: | http://hdl.handle.net/123456789/4554 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 2 (26). - 2018 |
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