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In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory. [ABSTRACT FROM AUTHOR]

An explicit categorical equivalence is defined between a proper subvariety of the class of PMV -algebras, as defined by Di Nola and Dvurečenskij, to be called PMV f -algebras, and the category of semi-low f u -rings. This categorical representation is done using the prime spectrum of the MV -algebras, through the equivalence between MV -algebras and l u -groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low f u -rings associated to Boolean algebras are characterized. [ABSTRACT FROM AUTHOR]