Жучок Анатолій Володимирович
http://hdl.handle.net/123456789/5804
Зав. кафедри, професор2024-03-29T01:36:19ZFree n-nilpotent dimonoids
http://hdl.handle.net/123456789/9028
Free n-nilpotent dimonoids
Zhuchok, A. V.
We construct a free n-nilpotent dimonoid and describe its structure. We also characterize the least n-nilpotent congruence on a free dimonoid, construct a new class of dimonoids
with zero and give examples of nilpotent dimonoids of nilpotency
index 2.
Zhuchok A. V. Free n-nilpotent dimonoids / A. V. Zhuchok // Algebra and Discrete Mathematics. - 2013. - Vol. 16, Number 2. - Рp. 299 – 310
2013-01-01T00:00:00ZFree (ℓr, rr)-dibands
http://hdl.handle.net/123456789/9027
Free (ℓr, rr)-dibands
Zhuchok, A. V.
Zhuchok A. V. Free (ℓr, rr)-dibands / A. V. Zhuchok // Algebra and Discrete Mathematics. - 2013. - Vol.15, Number 2. - Рp. 295-304.
2013-01-01T00:00:00ZFree n-dinilpotent doppelsemigroups
http://hdl.handle.net/123456789/9026
Free n-dinilpotent doppelsemigroups
Zhuchok, A. V.; Demko, M.
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.
Zhuchok A. V. Free n-dinilpotent doppelsemigroups / A. V. Zhuchok, M. Demko // Algebra and Discrete Mathematics. - 2016. - Vol. 22, Number 2. - Рр. 304–316.
2016-01-01T00:00:00ZFree products of dimonoids
http://hdl.handle.net/123456789/9025
Free products of dimonoids
Zhuchok, A. V.
We construct a free product of dimonoids which generalizes a free dimonoid presented
by J.-L. Loday and describe its structure.
Zhuchok A. V. Free products of dimonoids / A. V. Zhuchok // Quasigroups and Related Systems. - 2013. - № 21. - Pp. 273 − 278
2013-01-01T00:00:00Z