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Representations of ordered doppelsemigroups by binary relations

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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Main Authors: Zhuchok, Yurii, Koppitz, Jörg
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2019
Subjects:
doppelsemigroup
ordered doppelsemigroup
semigroup
binary relation
representation
17A30
06F05
43A65
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294
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spelling oai:ojs.admjournal.luguniv.edu.ua: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
institution Algebra and Discrete Mathematics
collection OJS
language English
topic doppelsemigroup
ordered doppelsemigroup
semigroup
binary relation
representation
17A30
06F05
43A65
spellingShingle doppelsemigroup
ordered doppelsemigroup
semigroup
binary relation
representation
17A30
06F05
43A65
Zhuchok, Yurii
Koppitz, Jörg
Representations of ordered doppelsemigroups by binary relations
topic_facet doppelsemigroup
ordered doppelsemigroup
semigroup
binary relation
representation
17A30
06F05
43A65
format Article
author Zhuchok, Yurii
Koppitz, Jörg
author_facet Zhuchok, Yurii
Koppitz, Jörg
author_sort Zhuchok, Yurii
title Representations of ordered doppelsemigroups by binary relations
title_short 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_sort representations of ordered doppelsemigroups by binary relations
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.
publisher Lugansk National Taras Shevchenko University
publishDate 2019
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1294
work_keys_str_mv AT zhuchokyurii representationsofordereddoppelsemigroupsbybinaryrelations
AT koppitzjorg representationsofordereddoppelsemigroupsbybinaryrelations
first_indexed 2024-04-12T06:26:03Z
last_indexed 2024-04-12T06:26:03Z
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