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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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2016
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543149578518528 |
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| author | Zhuchok, Anatolii V. Demko, Milan |
| author_facet | Zhuchok, Anatolii V. Demko, Milan |
| author_sort | Zhuchok, Anatolii V. |
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| collection | OJS |
| datestamp_date | 2016-12-31T09:22:47Z |
| 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. |
| first_indexed | 2026-02-08T07:57:52Z |
| format | Article |
| id | admjournalluguniveduua-article-312 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:52Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | Zhuchok, Anatolii V. Demko, Milan Free $n$-dinilpotent doppelsemigroups |
| title | Free $n$-dinilpotent doppelsemigroups |
| title_full | Free $n$-dinilpotent doppelsemigroups |
| title_fullStr | Free $n$-dinilpotent doppelsemigroups |
| title_full_unstemmed | Free $n$-dinilpotent doppelsemigroups |
| title_short | Free $n$-dinilpotent doppelsemigroups |
| title_sort | free $n$-dinilpotent doppelsemigroups |
| topic | |
| topic_facet | |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/312 |
| work_keys_str_mv | AT zhuchokanatoliiv freendinilpotentdoppelsemigroups AT demkomilan freendinilpotentdoppelsemigroups |