  An explicit categorical equivalence is defined between a proper subvariety of
the 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. 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. Besides
we show that class of $PMV_f$-algebras is coextensive.
