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,...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2018
Hauptverfasser: Zhuchok, A.V., Knauer, K.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/188415
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
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
id nasplib_isofts_kiev_ua-123456789-188415
record_format dspace
spelling Zhuchok, A.V.
Knauer, K.
2023-02-27T16:24:23Z
2023-02-27T16:24:23Z
2018
Abelian doppelsemigroups / A.V. Zhuchok, K. Knauer // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 290–304. — Бібліогр.: 31 назв. — англ.
1726-3255
2010 MSC: 08B20, 20M10, 20M50, 17A30.
https://nasplib.isofts.kiev.ua/handle/123456789/188415
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.
The paper was written during the research stay of the first author at the University of Aix-Marseille as a part of the French Government fellowship.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Abelian doppelsemigroups
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Abelian doppelsemigroups
spellingShingle Abelian doppelsemigroups
Zhuchok, A.V.
Knauer, K.
title_short Abelian doppelsemigroups
title_full Abelian doppelsemigroups
title_fullStr Abelian doppelsemigroups
title_full_unstemmed Abelian doppelsemigroups
title_sort abelian doppelsemigroups
author Zhuchok, A.V.
Knauer, K.
author_facet Zhuchok, A.V.
Knauer, K.
publishDate 2018
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description 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.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/188415
fulltext
citation_txt Abelian doppelsemigroups / A.V. Zhuchok, K. Knauer // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 290–304. — Бібліогр.: 31 назв. — англ.
work_keys_str_mv AT zhuchokav abeliandoppelsemigroups
AT knauerk abeliandoppelsemigroups
first_indexed 2025-11-25T20:57:21Z
last_indexed 2025-11-25T20:57:21Z
_version_ 1850539162313162752