On a product of universal hyperalgebras

We introduce and study a new operation of product of universal hyperalgebras which lies, with respect to set inclusion, between the cartesian product of the hyperalgebras and the cartesian product of their idempotent hulls. We give sufficient conditions for the validity of the first exponential law and a weak form of the second exponential law for the direct power of universal hyperalgebras with respect to the product introduced.