Geodesic
The ternary hyperidentities of associativity
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2003), pp. 36-44

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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.
Mots-clés : Reversible algebras
Keywords: hyperidentities. 
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L. R. Abramyan. The ternary hyperidentities of associativity. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2003), pp. 36-44. http://geodesic.mathdoc.fr/item/UZERU_2003_3_a5/