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 doppelsemigroup...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188491 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Interassociativity and three-element doppelsemigroups / V. Gavrylkiv, D. Rendziak // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 224–247. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532541841408000 |
|---|---|
| author | Gavrylkiv, V. Rendziak, D. |
| author_facet | Gavrylkiv, V. Rendziak, D. |
| citation_txt | Interassociativity and three-element doppelsemigroups / V. Gavrylkiv, D. Rendziak // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 224–247. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-24T05:05:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188491 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T05:05:37Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Gavrylkiv, V. Rendziak, D. 2023-03-02T19:24:26Z 2023-03-02T19:24:26Z 2019 Interassociativity and three-element doppelsemigroups / V. Gavrylkiv, D. Rendziak // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 224–247. — Бібліогр.: 20 назв. — англ. 1726-3255 2010 MSC: 08B20, 20M10, 20M50, 17A30. https://nasplib.isofts.kiev.ua/handle/123456789/188491 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. The authors would like to express their sincere thanks to the anonymous referee for a very careful reading of the paper and for all its insightful comments and valuable suggestions, which improve considerably the presentation of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Interassociativity and three-element doppelsemigroups Article published earlier |
| spellingShingle | Interassociativity and three-element doppelsemigroups Gavrylkiv, V. Rendziak, D. |
| title | 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_short | Interassociativity and three-element doppelsemigroups |
| title_sort | interassociativity and three-element doppelsemigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188491 |
| work_keys_str_mv | AT gavrylkivv interassociativityandthreeelementdoppelsemigroups AT rendziakd interassociativityandthreeelementdoppelsemigroups |