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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Бібліографічні деталі
Дата:2019
Автори: Zhuchok, Anatolii V., Knauer, Kolja
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2019
Теми:
Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1249
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-1249
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spelling admjournalluguniveduua-article-12492019-01-24T08:21:31Z Abelian doppelsemigroups Zhuchok, Anatolii V. Knauer, Kolja doppelsemigroup, abelian doppelsemigroup, free abelian doppelsemigroup, free doppelsemigroup, interassociativity, semigroup, congruence, doppelalgebra 08B20, 20M10, 20M50, 17A30 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. Lugansk National Taras Shevchenko University 2019-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1249 Algebra and Discrete Mathematics; Vol 26, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1249/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1249/430 Copyright (c) 2019 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2019-01-24T08:21:31Z
collection OJS
language English
topic doppelsemigroup
abelian doppelsemigroup
free abelian doppelsemigroup
free doppelsemigroup
interassociativity
semigroup
congruence
doppelalgebra
08B20
20M10
20M50
17A30
spellingShingle doppelsemigroup
abelian doppelsemigroup
free abelian doppelsemigroup
free doppelsemigroup
interassociativity
semigroup
congruence
doppelalgebra
08B20
20M10
20M50
17A30
Zhuchok, Anatolii V.
Knauer, Kolja
Abelian doppelsemigroups
topic_facet doppelsemigroup
abelian doppelsemigroup
free abelian doppelsemigroup
free doppelsemigroup
interassociativity
semigroup
congruence
doppelalgebra
08B20
20M10
20M50
17A30
format Article
author Zhuchok, Anatolii V.
Knauer, Kolja
author_facet Zhuchok, Anatolii V.
Knauer, Kolja
author_sort Zhuchok, Anatolii V.
title Abelian doppelsemigroups
title_short Abelian doppelsemigroups
title_full Abelian doppelsemigroups
title_fullStr Abelian doppelsemigroups
title_full_unstemmed Abelian doppelsemigroups
title_sort abelian doppelsemigroups
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 doppelsemigroup, give examples of abelian doppelsemigroups and find conditions under which the operations of an abelian doppelsemigroup coincide.
publisher Lugansk National Taras Shevchenko University
publishDate 2019
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1249
work_keys_str_mv AT zhuchokanatoliiv abeliandoppelsemigroups
AT knauerkolja abeliandoppelsemigroups
first_indexed 2025-12-02T15:29:56Z
last_indexed 2025-12-02T15:29:56Z
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