THE TERNARY HYPERIDENTITIES OF ASSOCIATIVITY

Abstract

The work is devoted to ternary hyperidentities of associativity, which are determined by the equality $((x, y, z), u, v) = (x, y, (z, u v))$. We get the following three hyperidentities: $$ X(Y(x, y, z), u, v) = Y(x, y, X(z, u, v)),  $$ $$X(X(x, y, z), u, v) = Y(x, y, Y(z, u, v)), $$ $$X(Y (x, y, z), u, v) = X (x, y, Y(z, u, v)).$$ The criteria of realization are proved for each of them in the reversible algebras.