QUANTALE-VALUED SUP-ALGEBRAS

Based on the notion of Q-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of Q-sup-algebras -- Q-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in \cite{zhang-laan}, we characterize their subalgebras and quotients, and following \cite{solovyov-qa}, we show that the category of Q-sup-algebras is isomorphic to a certain subcategory of a category of Q-modules.

Keywords:

Q-order , Q-sup-lattice , Q-ordered algebra , Q-sup-algebra , Quotient , subalgebra