Institutul de Matematică şi Informatică "Vladimir Andrunachievici"

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Subject: search.filters.subject.quasigroup

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    About Quadratic Functional Equations on Quasigroups [Articol]
    (2024) Sokhatsky, Fedir; Krainichuk, Halyna
    Functional equations over binary quasigroups are under consideration. An equation is called: quadratic, if each individual variable has either two appearances or none; cancellable, if a variable has two appearances and another none in a proper subterm; reducible, if it is equivalent to a system of equations such that every of which has less number of individual variables than the given one. Only the functional equations of unipotency, commutativity, associativity and mediality are noncancellable, and the irreducible ones are the same except the mediality. The criteria for the parastrophic equivalency of the equations up to the noncancellable equations were found.
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    About AC-Groupoids [Articol]
    (2024) Izbas, Vladimir; Izbas, Ana-Maria
    The concept of a right (left) AC-groupoid over an arbitrary group is defined and studied. Necessary and sufficient conditions which transform a right (left) AC-groupoid into a quasigroup are given. The AC-groupoids form a wide class of special groupoids and quasigroups that have a transitive subset of automorphisms.
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    Semisymmetric Quasigroups [Articol]
    (2024) Didurik, Natalia N.; Shcherbacov, Victor A.
    A quasigroup satisfying the identity x(yx) = y is called semisymmetric. In this article, the isotopy of semisimmetric quasigroups is studied. A condition is found when a loop, isotopic to a semisymmetric quasigroup, is a semisymmetric loop.
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    On a Method of Prolongation of Quasigroups [Articol]
    (2024) Cuznețov, Elena
    We consider a method of prolongation of finite quasigroups using two transversals, which intersect exactly in one cell, and study the recursive 1-differentiability of such prolongations.
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    Some Hash Functions Based on Quasigroups [Articol]
    (2024) Cernov, Vladimir; Shcherbacov, Victor
    In this paper, we consider the construction of hash functions based on finite quasigroups.
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    T-QUASIGROUPS WITH STEIN 2-ND AND 3-RD IDENTITY
    (2023) Shcherbacov, Victor; Radilova, Irina; Radilov, Petr
    In this paper we prolong research of T-quasigroups with Stein 2-rd (𝑥𝑦 · 𝑥 = 𝑦 · 𝑥𝑦) and Stein 3-rd (𝑥𝑦 · 𝑦𝑥 = 𝑦) identities [9].