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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Published in:Algebra and Discrete Mathematics
Date:2019
Main Authors: Zhuchok, Y.V., Koppitz, J.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/188428
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2025-12-07T20:55:16Z
format Article
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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