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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]

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli and Lettieri (Math Logic Q 1:27-43, ). [ABSTRACT FROM AUTHOR]