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: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543138630336512 |
|---|---|
| author | Gavrylkiv, Volodymyr Rendziak, Diana |
| author_facet | Gavrylkiv, Volodymyr Rendziak, Diana |
| author_sort | Gavrylkiv, Volodymyr |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-02-10T19:12:26Z |
| 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. |
| first_indexed | 2026-02-08T07:57:40Z |
| format | Article |
| id | admjournalluguniveduua-article-1427 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:40Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 Gavrylkiv, Volodymyr Rendziak, Diana Interassociativity and three-element doppelsemigroups |
| title | 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_short | Interassociativity and three-element doppelsemigroups |
| title_sort | interassociativity and three-element doppelsemigroups |
| topic | semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 |
| topic_facet | semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 |
| work_keys_str_mv | AT gavrylkivvolodymyr interassociativityandthreeelementdoppelsemigroups AT rendziakdiana interassociativityandthreeelementdoppelsemigroups |