DSpace Community:http://hdl.handle.net/123456789/58032024-03-28T12:24:44Z2024-03-28T12:24:44ZFree n-nilpotent dimonoidsZhuchok, A. V.http://hdl.handle.net/123456789/90282022-03-23T03:04:42Z2013-01-01T00:00:00ZTitle: Free n-nilpotent dimonoids
Authors: Zhuchok, A. V.
Abstract: 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.
Description: Zhuchok A. V. Free n-nilpotent dimonoids / A. V. Zhuchok // Algebra and Discrete Mathematics. - 2013. - Vol. 16, Number 2. - Рp. 299 – 3102013-01-01T00:00:00ZFree (ℓr, rr)-dibandsZhuchok, A. V.http://hdl.handle.net/123456789/90272022-03-23T03:05:00Z2013-01-01T00:00:00ZTitle: Free (ℓr, rr)-dibands
Authors: Zhuchok, A. V.
Description: 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 doppelsemigroupsZhuchok, A. V.Demko, M.http://hdl.handle.net/123456789/90262022-03-23T03:05:03Z2016-01-01T00:00:00ZTitle: Free n-dinilpotent doppelsemigroups
Authors: Zhuchok, A. V.; Demko, M.
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. 304–316.2016-01-01T00:00:00ZFree products of dimonoidsZhuchok, A. V.http://hdl.handle.net/123456789/90252022-03-23T03:05:21Z2013-01-01T00:00:00ZTitle: Free products of dimonoids
Authors: Zhuchok, A. V.
Abstract: We construct a free product of dimonoids which generalizes a free dimonoid presented
by J.-L. Loday and describe its structure.
Description: Zhuchok A. V. Free products of dimonoids / A. V. Zhuchok // Quasigroups and Related Systems. - 2013. - № 21. - Pp. 273 − 2782013-01-01T00:00:00Z