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

A new class of $MV$-algebras with product, called L$\Pi_q$-algebras, has been introduced. In these algebras, the discontinuous product residuation $\to_\pi$  is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need ofexpressiveness and the need of continuity of connectives.  Following a good tradition in many-valued logic, 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 L$\Pi_q$-algebras and of $f$-quasifields are equivalent.

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

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