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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188428 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Representations of ordered doppelsemigroups by binary relations / Y.V. Zhuchok, J. Koppitz // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 144–154. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748284180758528 |
|---|---|
| author | Zhuchok, Y.V. Koppitz, J. |
| author_facet | Zhuchok, Y.V. Koppitz, J. |
| citation_txt | Representations of ordered doppelsemigroups by binary relations / Y.V. Zhuchok, J. Koppitz // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 144–154. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T20:55:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188428 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:55:16Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zhuchok, Y.V. Koppitz, J. 2023-02-28T19:28:02Z 2023-02-28T19:28:02Z 2019 Representations of ordered doppelsemigroups by binary relations / Y.V. Zhuchok, J. Koppitz // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 144–154. — Бібліогр.: 20 назв. — англ. 1726-3255 2010 MSC: 17A30, 06F05, 43A65. https://nasplib.isofts.kiev.ua/handle/123456789/188428 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. The paper was written during the research stay of the first author at the Potsdam University in the frame of the Programme of German Academic Exchange Service (DAAD). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Representations of ordered doppelsemigroups by binary relations Article published earlier |
| spellingShingle | Representations of ordered doppelsemigroups by binary relations Zhuchok, Y.V. Koppitz, J. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188428 |
| work_keys_str_mv | AT zhuchokyv representationsofordereddoppelsemigroupsbybinaryrelations AT koppitzj representationsofordereddoppelsemigroupsbybinaryrelations |