Abstract

It is given an explicit description of coproducts in the category of Kleene algebras in terms of the dual topological spaces. As an application, a description of dual spaces of free Kleene algebras is given. It is also shown that the coproduct of a family of three-valued ukasiewicz algebras in the category of Kleene algebras is the same as the coproduct in the subcategory of three-valued ukasiewicz algebras.