MV -algebras were introduced by Chang to prove the completeness of the infinite-valued Lukasiewicz propositional calculus. In this paper we give a categorical equivalence between the varieties of (n + 1)-valued MV-algebras and the classes of Boolean algebras endowed with a certain family of filters. An- other similar categorical equivalence is given by A. Di Nola and A. Lettieri. Also, we point out the relations between this categor- ical equivalence and the duality established by R. Cignoli, which can be derived from results obtained by P. Niederkorn on natural dualities for varieties of MV -algebras.
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