Direct Powers of Hyperalgebras Carried by Good Homomorphisms

Abstract

In the present paper, we study the direct power of hyperalgebras obtained as the subhyperalgebra of their direct product carried by good homomorphisms. We give sufficient conditions for the validity of the second exponential law and a weak form of the first exponential law. Moreover, we restrict the concepts of the direct powers from hyperalgebras to algebras and give sufficient conditions for the validity of the first and the second exponential laws for algebras.