A classification of quasigroup functional equations of the type (3; 3; 0).

Abstract

In this article, the results of the classification of generalized quasigroup functional equations with two, three, and four functional variables are systematized. Generalized quasigroup functional equations of the type (3; 3; 0) are classified, as a result, 6 classes are obtained. Pairwise parastrophically-primary non-equivalence of representatives of classes, and therefore of the classes themselves, is partially established. Identities that define the inverse function (quasigroup) are called primary. Conversions of functional equations using these identities are also called primary. Two functional equations are called primarily (parastrophically) equivalent, if you can go from one equation to another with the help of the finite number of applications of the primary transformations. A type (an individual type) of functional equation with k individual variables is called a kit m1;m2; : : : ;mk , where mi is the number of occurrences in the equation i - this individual variable.