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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| Видавець: | Lugansk National Taras Shevchenko University |
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2173 |
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Організація
Algebra and Discrete Mathematics| Резюме: | 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. |
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