$Structure of relatively free $n$-tuple semigroups$

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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Дата:	2023
Автор:	Zhuchok, A. V.
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2023
Теми:	$n$-tuple semigroup free $n$-tuple semigroup relatively free $n$-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-2173
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua: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
institution	Algebra and Discrete Mathematics
collection	OJS
language	English
topic	$n$-tuple semigroup free $n$-tuple semigroup relatively free $n$-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99
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
topic_facet	$n$-tuple semigroup free $n$-tuple semigroup relatively free $n$-tuple semigroup semigroup 08B20 20M10 20M50 17A30 17D99
format	Article
author	Zhuchok, A. V.
author_facet	Zhuchok, A. V.
author_sort	Zhuchok, A. V.
title	Structure of relatively free $n$-tuple semigroups
title_short	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_sort	structure of relatively free $n$-tuple semigroups
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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2023
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173
work_keys_str_mv	AT zhuchokav structureofrelativelyfreentuplesemigroups
first_indexed	2024-04-12T06:27:39Z
last_indexed	2024-04-12T06:27:39Z
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Structure of relatively free \(n\)-tuple semigroups

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