On the power-set $$Q$$ Q -algebras

Abstract

$$Q$$ -algebras form an important class of ordered algebraic structures, which can be regarded as a generalization of quantales and $$Q$$ -modules, and play an important role in the study of lattice-valued quantales, lattice-valued frames and stratified lattice-valued topological spaces. Every $$Q$$ -algebra is isomorphic to a quotient $$Q$$ -algebra of some power-set $$Q$$ -algebra. We investigate some properties of power-set $$Q$$ -algebras, and, by means of the relations between ordered semigroups, give a general characterization for the strong homomorphisms between power-set $$Q$$ -algebras.