Structure of relatively free \(n\)-tuple semigroups
An \(n\)-tuple semigroup is an algebra defined on a set with \(n\) binary associative operations. This notion was considered by Koreshkov in the context of the theory of \(n\)-tuple algebras of associative type. The \(n > 1\) pairwise interassociative semigroups give rise to an \(n\)-tuple se...
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2023
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543144741437440 |
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| author | Zhuchok, A. V. |
| author_facet | Zhuchok, A. V. |
| author_sort | Zhuchok, A. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-12-11T16:21:07Z |
| description | An \(n\)-tuple semigroup is an algebra defined on a set with \(n\) binary associative operations. This notion was considered by Koreshkov in the context of the theory of \(n\)-tuple algebras of associative type. The \(n > 1\) pairwise interassociative semigroups give rise to an \(n\)-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of \(n\)-tuple semigroups. We present the constructions of the free \(n\)-tuple semigroup, the free commutative \(n\)-tuple semigroup, the free rectangular \(n\)-tuple semigroup, the free left (right) \(k\)-nilpotent \(n\)-tuple semigroup, the free \(k\)-nilpotent \(n\)-tuple semigroup, and the free weakly \(k\)-nilpotent \(n\)-tuple semigroup. Some of these results can be applied to constructing relatively free cubical trialgebras and doppelalgebras. |
| first_indexed | 2026-02-08T07:57:48Z |
| format | Article |
| id | admjournalluguniveduua-article-2173 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:48Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-21732023-12-11T16:21:07Z Structure of relatively free \(n\)-tuple semigroups Zhuchok, A. V. \(n\)-tuple semigroup, free \(n\)-tuple semigroup, relatively free \(n\)-tuple semigroup, semigroup 08B20, 20M10, 20M50, 17A30, 17D99 An \(n\)-tuple semigroup is an algebra defined on a set with \(n\) binary associative operations. This notion was considered by Koreshkov in the context of the theory of \(n\)-tuple algebras of associative type. The \(n > 1\) pairwise interassociative semigroups give rise to an \(n\)-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of \(n\)-tuple semigroups. We present the constructions of the free \(n\)-tuple semigroup, the free commutative \(n\)-tuple semigroup, the free rectangular \(n\)-tuple semigroup, the free left (right) \(k\)-nilpotent \(n\)-tuple semigroup, the free \(k\)-nilpotent \(n\)-tuple semigroup, and the free weakly \(k\)-nilpotent \(n\)-tuple semigroup. Some of these results can be applied to constructing relatively free cubical trialgebras and doppelalgebras. Lugansk National Taras Shevchenko University 2023-12-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173 10.12958/adm2173 Algebra and Discrete Mathematics; Vol 36, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| spellingShingle | \(n\)-tuple semigroup free \(n\)-tuple semigroup relatively free \(n\)-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99 Zhuchok, A. V. Structure of relatively free \(n\)-tuple semigroups |
| title | Structure of relatively free \(n\)-tuple semigroups |
| title_full | Structure of relatively free \(n\)-tuple semigroups |
| title_fullStr | Structure of relatively free \(n\)-tuple semigroups |
| title_full_unstemmed | Structure of relatively free \(n\)-tuple semigroups |
| title_short | Structure of relatively free \(n\)-tuple semigroups |
| title_sort | structure of relatively free \(n\)-tuple semigroups |
| topic | \(n\)-tuple semigroup free \(n\)-tuple semigroup relatively free \(n\)-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99 |
| topic_facet | \(n\)-tuple semigroup free \(n\)-tuple semigroup relatively free \(n\)-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173 |
| work_keys_str_mv | AT zhuchokav structureofrelativelyfreentuplesemigroups |