Continuous approximations of MV-algebras with product and product residuation: a category-theoretic equivalence

In [9] a new class of MV -algebras with product, called LΠqalgebras, has been introduced. In these algebras, the discontinuous product residuation →π defined in [4] is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need of expressiveness and the need of continuity of connectives. Following a good tradition in many-valued logic (see e.g. [10], [7], [3] and [8]), in this paper we introduce a class of commutative f -rings with strong unit and with a sort of weak divisibility property, called f -quasifields, and we show that the categories of LΠq-algebras and of f -quasifields are equivalent.