Interassociativity and three-element doppelsemigroups
In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigro...
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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-14272020-02-10T19:12:26Z Interassociativity and three-element doppelsemigroups Gavrylkiv, Volodymyr Rendziak, Diana semigroup, interassociativity, doppelsemigroup, strong doppelsemigroup 08B20, 20M10, 20M50, 17A30 In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into 17 pairs of dual doppelsemigroups. Also up to isomorphism there are 65 strong doppelsemigroups of order 3, and all non-strong doppelsemigroups are not commutative. Lugansk National Taras Shevchenko University 2020-02-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 Algebra and Discrete Mathematics; Vol 28, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1427/640 Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 |
| spellingShingle |
semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 Gavrylkiv, Volodymyr Rendziak, Diana Interassociativity and three-element doppelsemigroups |
| topic_facet |
semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 |
| format |
Article |
| author |
Gavrylkiv, Volodymyr Rendziak, Diana |
| author_facet |
Gavrylkiv, Volodymyr Rendziak, Diana |
| author_sort |
Gavrylkiv, Volodymyr |
| title |
Interassociativity and three-element doppelsemigroups |
| title_short |
Interassociativity and three-element doppelsemigroups |
| title_full |
Interassociativity and three-element doppelsemigroups |
| title_fullStr |
Interassociativity and three-element doppelsemigroups |
| title_full_unstemmed |
Interassociativity and three-element doppelsemigroups |
| title_sort |
interassociativity and three-element doppelsemigroups |
| description |
In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into 17 pairs of dual doppelsemigroups. Also up to isomorphism there are 65 strong doppelsemigroups of order 3, and all non-strong doppelsemigroups are not commutative. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 |
| work_keys_str_mv |
AT gavrylkivvolodymyr interassociativityandthreeelementdoppelsemigroups AT rendziakdiana interassociativityandthreeelementdoppelsemigroups |
| first_indexed |
2024-04-12T06:26:04Z |
| last_indexed |
2024-04-12T06:26:04Z |
| _version_ |
1796109148780232704 |