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An explicit categorical equivalence is defined between a proper subvariety ofthe class of $PMV$-algebras, as defined by Di Nola and Dvure$\check{c}$enskij,to be called $PMV_f$-algebras, and the category of semi-low $f_u$-rings. Thiscategorical representation is done using the prime spectrum of the$MV$-algebras, through the equivalence between $MV$-algebras and $l_u$-groupsestablished by Mundici, from the perspective of the Dubuc-Poveda approach, thatextends the construction defined by Chang on chains. As a particular case,semi-low $f_u$-rings associated to Boolean algebras are characterized. Besideswe show that class of $PMV_f$-algebras is coextensive.

Categorical Equivalence between $PMV_f$- product algebras and semi-low $f_u$-rings