Перегляд за автором "Zhuchok, A.V."

Сортувати за: Порядок: Результатів:

  • Abelian doppelsemigroups 
    Zhuchok, A.V.; Knauer, K. (Algebra and Discrete Mathematics, 2018)
    A doppelsemigroup is an algebraic system consisting of a set with two binary associative operations satisfying certain identities. Doppelsemigroups are a generalization of semigroups and they have relationships with such ...
  • Commutative dimonoids 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2009)
    We present some congruence on the dimonoid with a commutative operation and use it to obtain a decomposition of a commutative dimonoid.
  • Free commutative dimonoids 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2010)
    We construct a free commutative dimonoid and characterize the least idempotent congruence on this dimonoid.
  • Free n-dinilpotent doppelsemigroups 
    Zhuchok, A.V.; Demko, M. (Algebra and Discrete Mathematics, 2016)
    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 ...
  • Free n-nilpotent dimonoids 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2013)
    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 ...
  • Free normal dibands 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2011)
    We construct a free normal diband, a free (ℓn,n)-diband, a free (n,rn)-diband and a free (ℓn,rn)-diband. We also describe the structure of free normal dibands and characterize some least congruences on these dibands.
  • Free rectangular dibands and free dimonoids 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2011)
    We construct a free rectangular diband and describe its structure. We also present the least rectangular diband congruence, the least (rb,rz)-congruence, the least left zero and right zero congruence, the least rectangular ...
  • Free (ℓr, rr)-dibands 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2013)
    We prove that varieties of (ℓr, rr)-dibands and (ℓn, rn)-dibands coincide and describe the structure of free (ℓr, rr)-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, ...
  • Structure of relatively free trioids 
    Zhuchok, A.V. (Algebra and Discrete Mathematics, 2021)
    Loday and Ronco introduced the notions of a trioid and a trialgebra, and constructed the free trioid of rank 1 and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the ...
  • Tribands of subtrioids 
    Zhuchok, A.V. (Труды Института прикладной математики и механики, 2010)
    We introduce the notion of a triband of subtrioids and prove that every trioid with a commutative periodic semigroup is a semilattice of unipotent subtrioids. Also we give examples of trioids which are decomposed into a ...