Weakly Divisible MV-Algebras and Product

We introduce weakly divisible MV-algebras and we show that every weakly divisible s-complete MV-algebra is isomorphic to the system of all continuous fuzzy functions defined on some compact Hausdorff space which generalizes a result of Di Nola and Sesse in ‘‘Non Classical Logics and Their Application to Fuzzy Subsets,’’ Kluwer Academic, Dordrecht, to appear.. This enables us to define an associative and commutative product on weakly divisible s-complete MV-algebras with a multiplicative unity 1. As an application, we show that any system of observables on this MV-algebra admits a joint observable with respect to this product.