Free $n$-dinilpotent doppelsemigroups
A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic $K$-theory. In this paper we consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgeb...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2016
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-3122016-12-31T09:22:47Z Free $n$-dinilpotent doppelsemigroups Zhuchok, Anatolii V. Demko, Milan A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic $K$-theory. In this paper we consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. We construct a free $n$-dinilpotent doppelsemigroupand study separately free $n$-dinilpotent doppelsemigroups of rank $1$. Moreover, we characterize the least $n$-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the free $n$-dinilpotent doppelsemigroup are isomorphic and the automorphism group of the free $n$-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups and prove that a system of axioms of a doppelsemigroup is independent. Lugansk National Taras Shevchenko University 2016-12-31 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312 Algebra and Discrete Mathematics; Vol 22, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2016-12-31T09:22:47Z |
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English |
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Zhuchok, Anatolii V. Demko, Milan Free $n$-dinilpotent doppelsemigroups |
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Article |
| author |
Zhuchok, Anatolii V. Demko, Milan |
| author_facet |
Zhuchok, Anatolii V. Demko, Milan |
| author_sort |
Zhuchok, Anatolii V. |
| title |
Free $n$-dinilpotent doppelsemigroups |
| title_short |
Free $n$-dinilpotent doppelsemigroups |
| title_full |
Free $n$-dinilpotent doppelsemigroups |
| title_fullStr |
Free $n$-dinilpotent doppelsemigroups |
| title_full_unstemmed |
Free $n$-dinilpotent doppelsemigroups |
| title_sort |
free $n$-dinilpotent doppelsemigroups |
| description |
A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic $K$-theory. In this paper we consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. We construct a free $n$-dinilpotent doppelsemigroupand study separately free $n$-dinilpotent doppelsemigroups of rank $1$. Moreover, we characterize the least $n$-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the free $n$-dinilpotent doppelsemigroup are isomorphic and the automorphism group of the free $n$-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups and prove that a system of axioms of a doppelsemigroup is independent. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312 |
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2025-07-17T10:31:13Z |
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