Эта публикация цитируется в
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RESEARCH ARTICLE
Free $n$-dinilpotent doppelsemigroups
Anatolii V. Zhuchoka,
Milan Demkob a Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol square, 1, Starobilsk, 92703, Ukraine
b Department of Physics, Mathematics and Techniques, University of Presov, Slovakia, 17. novembra 1, Presov, 08116, Slovakia
Аннотация:
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.
Ключевые слова:
doppelalgebra, interassociativity, doppelsemigroup, free
$n$-dinilpotent doppelsemigroup, free doppelsemigroup, semigroup, congruence.
MSC: 08B20,
20M10,
20M50,
17A30 Поступила в редакцию: 03.10.2016
Исправленный вариант: 30.11.2016
Язык публикации: английский