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,...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| 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| _version_ | 1862551199689998336 |
|---|---|
| author | Zhuchok, A.V. Knauer, K. |
| author_facet | Zhuchok, A.V. Knauer, K. |
| citation_txt | Abelian doppelsemigroups / A.V. Zhuchok, K. Knauer // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 290–304. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-25T20:57:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188415 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T20:57:21Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Abelian doppelsemigroups Zhuchok, A.V. Knauer, K. |
| title | Abelian doppelsemigroups |
| title_full | Abelian doppelsemigroups |
| title_fullStr | Abelian doppelsemigroups |
| title_full_unstemmed | Abelian doppelsemigroups |
| title_short | Abelian doppelsemigroups |
| title_sort | abelian doppelsemigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188415 |
| work_keys_str_mv | AT zhuchokav abeliandoppelsemigroups AT knauerk abeliandoppelsemigroups |