On Some Associative Formula with Functional Variables

摘要

In work of Movsisyan and Gevorgyan [1], it was proved that the reversible algebra (Q, Sigma) satisfying the following second-order formulafor all X, Y, there exists X', Y'for all x, y, z(X(Y' (x, y), z) = Y(x, X'(y, z))),is linear over the group. In the current work a more general result is proved that the regular and division algebra (Q, Sigma) with the mentioned second-order formula is endolinear over the group.