In this paper we shall prove thatl-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterizel-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation betweenl-ideals inl-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to thef-rings.