Representations of ordered doppelsemigroups by binary relations
We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particul...
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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543335066370048 |
|---|---|
| author | Zhuchok, Yurii Koppitz, Jörg |
| author_facet | Zhuchok, Yurii Koppitz, Jörg |
| author_sort | Zhuchok, Yurii |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-03-23T17:44:10Z |
| description | We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particular, we obtain an analogue of Cayley's theorem for semigroups in the class of doppelsemigroups. We also describe the representations of ordered doppelsemigroups by binary transitive relations. |
| first_indexed | 2026-02-08T07:57:36Z |
| format | Article |
| id | admjournalluguniveduua-article-1294 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:36Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-12942019-03-23T17:44:10Z Representations of ordered doppelsemigroups by binary relations Zhuchok, Yurii Koppitz, Jörg doppelsemigroup, ordered doppelsemigroup, semigroup, binary relation, representation 17A30, 06F05, 43A65 We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particular, we obtain an analogue of Cayley's theorem for semigroups in the class of doppelsemigroups. We also describe the representations of ordered doppelsemigroups by binary transitive relations. Lugansk National Taras Shevchenko University 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294/pdf Copyright (c) 2019 Algebra and Discrete Mathematics |
| spellingShingle | doppelsemigroup ordered doppelsemigroup semigroup binary relation representation 17A30 06F05 43A65 Zhuchok, Yurii Koppitz, Jörg Representations of ordered doppelsemigroups by binary relations |
| title | Representations of ordered doppelsemigroups by binary relations |
| title_full | Representations of ordered doppelsemigroups by binary relations |
| title_fullStr | Representations of ordered doppelsemigroups by binary relations |
| title_full_unstemmed | Representations of ordered doppelsemigroups by binary relations |
| title_short | Representations of ordered doppelsemigroups by binary relations |
| title_sort | representations of ordered doppelsemigroups by binary relations |
| topic | doppelsemigroup ordered doppelsemigroup semigroup binary relation representation 17A30 06F05 43A65 |
| topic_facet | doppelsemigroup ordered doppelsemigroup semigroup binary relation representation 17A30 06F05 43A65 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294 |
| work_keys_str_mv | AT zhuchokyurii representationsofordereddoppelsemigroupsbybinaryrelations AT koppitzjorg representationsofordereddoppelsemigroupsbybinaryrelations |