Mathematics

The ternary hyperidentities of associativity

L. R. Abramyan

Yerevan State University

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.

Keywords: Reversible algebras, hyperidentities.

UDC: 519.48

Received: 11.02.2003
Accepted: 09.10.2003