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
Date:2016
Main Authors: Zhuchok, A.V., Demko, M.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2016
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
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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.
ISSN:1726-3255