Interassociativity and three-element doppelsemigroups

In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigro...

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Date:	2020
Main Authors:	Gavrylkiv, Volodymyr, Rendziak, Diana
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2020
Subjects:	semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427
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Journal Title:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-1427
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spelling	oai:ojs.admjournal.luguniv.edu.ua:article-14272020-02-10T19:12:26Z Interassociativity and three-element doppelsemigroups Gavrylkiv, Volodymyr Rendziak, Diana semigroup, interassociativity, doppelsemigroup, strong doppelsemigroup 08B20, 20M10, 20M50, 17A30 In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into 17 pairs of dual doppelsemigroups. Also up to isomorphism there are 65 strong doppelsemigroups of order 3, and all non-strong doppelsemigroups are not commutative. Lugansk National Taras Shevchenko University 2020-02-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427 Algebra and Discrete Mathematics; Vol 28, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1427/640 Copyright (c) 2020 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2020-02-10T19:12:26Z
collection	OJS
language	English
topic	semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30
spellingShingle	semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30 Gavrylkiv, Volodymyr Rendziak, Diana Interassociativity and three-element doppelsemigroups
topic_facet	semigroup interassociativity doppelsemigroup strong doppelsemigroup 08B20 20M10 20M50 17A30
format	Article
author	Gavrylkiv, Volodymyr Rendziak, Diana
author_facet	Gavrylkiv, Volodymyr Rendziak, Diana
author_sort	Gavrylkiv, Volodymyr
title	Interassociativity and three-element doppelsemigroups
title_short	Interassociativity and three-element doppelsemigroups
title_full	Interassociativity and three-element doppelsemigroups
title_fullStr	Interassociativity and three-element doppelsemigroups
title_full_unstemmed	Interassociativity and three-element doppelsemigroups
title_sort	interassociativity and three-element doppelsemigroups
description	In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into 17 pairs of dual doppelsemigroups. Also up to isomorphism there are 65 strong doppelsemigroups of order 3, and all non-strong doppelsemigroups are not commutative.
publisher	Lugansk National Taras Shevchenko University
publishDate	2020
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1427
work_keys_str_mv	AT gavrylkivvolodymyr interassociativityandthreeelementdoppelsemigroups AT rendziakdiana interassociativityandthreeelementdoppelsemigroups
first_indexed	2025-07-17T10:30:58Z
last_indexed	2025-07-17T10:30:58Z
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Interassociativity and three-element doppelsemigroups

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