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 doppelalgebra...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155735 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Free n-dinilpotent doppelsemigroups / A.V. Zhuchok, M. Demko // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 304-316. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719939534651392 |
|---|---|
| author | Zhuchok, A.V. Demko, M. |
| author_facet | Zhuchok, A.V. Demko, M. |
| citation_txt | Free n-dinilpotent doppelsemigroups / A.V. Zhuchok, M. Demko // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 304-316. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 freen-dinilpotent doppelsemigroup and study separately freen-dinilpotentdoppelsemigroups of rank 1. Moreover,we characterize the least n-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the freen-dinilpotentdoppelsemigroup are isomorphic and the automorphism group of the freen-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups andprove that a system of axioms of a doppelsemigroup is independent.
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| first_indexed | 2025-12-07T18:23:00Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-155735 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:23:00Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zhuchok, A.V. Demko, M. 2019-06-17T11:32:32Z 2019-06-17T11:32:32Z 2016 Free n-dinilpotent doppelsemigroups / A.V. Zhuchok, M. Demko // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 304-316. — Бібліогр.: 23 назв. — англ. 1726-3255 2010 MSC:08B20, 20M10, 20M50, 17A30. https://nasplib.isofts.kiev.ua/handle/123456789/155735 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 freen-dinilpotent doppelsemigroup and study separately freen-dinilpotentdoppelsemigroups of rank 1. Moreover,we characterize the least n-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the freen-dinilpotentdoppelsemigroup are isomorphic and the automorphism group of the freen-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups andprove that a system of axioms of a doppelsemigroup is independent. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Free n-dinilpotent doppelsemigroups Article published earlier |
| spellingShingle | Free n-dinilpotent doppelsemigroups Zhuchok, A.V. Demko, M. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155735 |
| work_keys_str_mv | AT zhuchokav freendinilpotentdoppelsemigroups AT demkom freendinilpotentdoppelsemigroups |