http://hdl.handle.net/123456789/5804 Зав. кафедри, професор Thu, 16 Apr 2026 00:51:41 GMT 2026-04-16T00:51:41Z 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 Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/123456789/9028 2013-01-01T00:00:00Z 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. Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/123456789/9027 2013-01-01T00:00:00Z 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. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/123456789/9026 2016-01-01T00:00:00Z 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 Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/123456789/9025 2013-01-01T00:00:00Z