Solution and full classification of generalized binary functional equations of the type (3; 3; 0)
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KRAINICHUK, Halyna, SOKHATSKY, Fedir M.. Solution and full classification of generalized binary functional equations of the type (3; 3; 0). In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, nr. 2(87), pp. 41-53. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(87) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322

Solution and full classification of generalized binary functional equations of the type (3; 3; 0)

CZU: 512.548
MSC 2010: 34C05, 58F14.

Pag. 41-53

Krainichuk Halyna, Sokhatsky Fedir M.
 
Vasyl Stus Donetsk National University
 
 
Disponibil în IBN: 2 decembrie 2018


Rezumat

Generalized binary functional quasigroup equations in two individual variables with three appearances are under consideration. There exist five classes of the equations (two equations belong to the same class if there exists a relation between sets of their solutions). The quasigroup solution sets of equations from every class are given. In addition, it is proved that every parastrophe of a quasigroup has an orthogonal mate if the quasigroup has an orthogonal mate.

Cuvinte-cheie
quasigroup, functional equation, quasigroup solution, invariant, parastrophic equivalence, orthogonal mate, Latin square., identity