On a product of universal hyperalgebras
Abstract 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.
On exponentiation of universal hyperalgebras
Abstract. For universal hyperalgebras we study a binary operation of exponentiation which to a pair of universal hyperalgebras of a given type assigns their power, i.e., a universal hyperalgebra of the same type carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of universal hyperalgebras of the same type and homomorphisms between them.
Mono-unary algebras in the work of Czechoslovak mathematicians
In 1950, O. Boruvka formulated a problem that led to study homomorphisms of mono-unary algebras. His problem stimulated the investigation of these algebras in Czechoslovakia. This article includes a brief survey of typical results obtained by.Czechoslovak mathematicians in this area.