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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, Y.V., Koppitz, J.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2019
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/188428
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spelling irk-123456789-1884282023-03-01T01:27:05Z Representations of ordered doppelsemigroups by binary relations Zhuchok, Y.V. Koppitz, J. 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. 2019 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188428 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Zhuchok, Y.V.
Koppitz, J.
spellingShingle Zhuchok, Y.V.
Koppitz, J.
Representations of ordered doppelsemigroups by binary relations
Algebra and Discrete Mathematics
author_facet Zhuchok, Y.V.
Koppitz, J.
author_sort Zhuchok, Y.V.
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
publisher Інститут прикладної математики і механіки НАН України
publishDate 2019
url http://dspace.nbuv.gov.ua/handle/123456789/188428
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.
series Algebra and Discrete Mathematics
work_keys_str_mv AT zhuchokyv representationsofordereddoppelsemigroupsbybinaryrelations
AT koppitzj representationsofordereddoppelsemigroupsbybinaryrelations
first_indexed 2023-10-18T23:08:20Z
last_indexed 2023-10-18T23:08:20Z
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