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 |
| Published: |
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| Summary: | 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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| ISSN: | 1726-3255 |