2018
Том 70
№ 2

All Issues

Sokhats’kyi F. M.

Articles: 2
Article (Ukrainian)

On the classification of functional equations on quasigroups

Sokhats’kyi F. M.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Abstract Characteristic of the Class of Unitary Positional Algebras of Operations

Sokhats’kyi F. M.

↓ Abstract   |   Full text (.pdf)

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.