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http://hdl.handle.net/123456789/9026
Title: | Free n-dinilpotent doppelsemigroups |
Authors: | Zhuchok, A. V. Demko, M. |
Issue Date: | 2016 |
Abstract: | 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 doppelsemigroup and 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. |
Description: | Zhuchok A. V. Free n-dinilpotent doppelsemigroups / A. V. Zhuchok, M. Demko // Algebra and Discrete Mathematics. - 2016. - Vol. 22, Number 2. - Рр. 304–316. |
URI: | http://hdl.handle.net/123456789/9026 |
Appears in Collections: | Жучок Анатолій Володимирович |
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2016_Eng_24.pdf | 323.6 kB | Adobe PDF | View/Open |
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