Sokhats’kyi F. M.
Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1259-1266
We consider functional equations over quasigroup operations. We prove that every quadratic parastrophically uncancelable functional equation for four object variables is parastrophically equivalent to the functional equation of mediality or the functional equation of pseudomediality. The set of all solutions of the general functional equation of pseudomediality is found and a criterion for the uncancelability of a quadratic functional equation for four object variables is established.
Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 961-968
We find an abstract characteristic of the class of unitary positional algebras of operations, i.e., algebras that contain a complete collection of selectors.
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 251-259
We describe normal congruences of group isotopes, establish criteria of homomorphism and isomorphism, and select the methods for description of isotopes up to isomorphism. In addition, we establish a criterion for a subset to be a subquasigroup of a group isotope and describe subquasigroups of certain classes of group isotopes. The obtained results are applied to the investigation of left distributive quasi-groups.
Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1692–1703
We select canonical decompositions of the isotopes of groups, show that they are unique, and establish relationships between them. We also obtain external characteristics of the identities which imply the linearity or alinearity of the isotopy and the commutativity of the corresponding group. We describe the identities of linear isotopes of Abelian groups, i.e., ofT-quasigroups, and suggest a new method for the description of isotopic closures of classes of groups.