Geodesic
Abelian doppelsemigroups
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 290-304

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : doppelalgebra. 
@article{ADM_2018_26_2_a7,
     author = {Anatolii V. Zhuchok and Kolja Knauer},
     title = {Abelian doppelsemigroups},
     journal = {Algebra and discrete mathematics},
     pages = {290--304},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a7/}
}
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Anatolii V. Zhuchok; Kolja Knauer. Abelian doppelsemigroups. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 290-304. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a7/