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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| Дата: | 2019 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2019
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| 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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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 |
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Algebra and Discrete Mathematics |
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| 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 |
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AT zhuchokanatoliiv abeliandoppelsemigroups AT knauerkolja abeliandoppelsemigroups |
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2025-12-02T15:29:56Z |
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2025-12-02T15:29:56Z |
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1850412212721549312 |