Note on cyclic doppelsemigroups
A~doppelsemigroup \((G,\dashv,\vdash)\) is called cyclic if \((G,\dashv)\) is a~cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist \(\tau(n)\) finite cyclic (strong) doppelsemigroups of order \(n\), where \(\tau...
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1991 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
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oai:ojs.admjournal.luguniv.edu.ua:article-19912023-02-08T16:55:57Z Note on cyclic doppelsemigroups Gavrylkiv, V. semigroup, interassociativity, doppelsemigroup, strong doppelsemigroup 08B20, 20M10, 20M50, 17A30 A~doppelsemigroup \((G,\dashv,\vdash)\) is called cyclic if \((G,\dashv)\) is a~cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist \(\tau(n)\) finite cyclic (strong) doppelsemigroups of order \(n\), where \(\tau\) is the number of divisors function. Also there exist infinite countably many pairwise non-isomorphic infinite cyclic (strong) doppelsemigroups. Lugansk National Taras Shevchenko University 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1991 10.12958/adm1991 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1991/pdf Copyright (c) 2023 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, V. Note on cyclic doppelsemigroups |
| topic_facet |
semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 |
| format |
Article |
| author |
Gavrylkiv, V. |
| author_facet |
Gavrylkiv, V. |
| author_sort |
Gavrylkiv, V. |
| title |
Note on cyclic doppelsemigroups |
| title_short |
Note on cyclic doppelsemigroups |
| title_full |
Note on cyclic doppelsemigroups |
| title_fullStr |
Note on cyclic doppelsemigroups |
| title_full_unstemmed |
Note on cyclic doppelsemigroups |
| title_sort |
note on cyclic doppelsemigroups |
| description |
A~doppelsemigroup \((G,\dashv,\vdash)\) is called cyclic if \((G,\dashv)\) is a~cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist \(\tau(n)\) finite cyclic (strong) doppelsemigroups of order \(n\), where \(\tau\) is the number of divisors function. Also there exist infinite countably many pairwise non-isomorphic infinite cyclic (strong) doppelsemigroups. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1991 |
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AT gavrylkivv noteoncyclicdoppelsemigroups |
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2024-04-12T06:25:41Z |
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2024-04-12T06:25:41Z |
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