Abstract

$MV-$algebras were introduced by Chang to prove the completeness of the infinite-valued {\L}ukasiewicz propositional calculus. In this paper we give a categorical equi\-va\-lence between the varieties of $-$valued MV-algebras and the classes of Boolean algebras endowed with a certain family of filters. Another similar categorical equi\-va\-lence is given by A. Di Nola and A. Lettieri. Also, we point out the relations between this categorical 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.}