new characterization theorems of the mp-quantales

The mp-quantales were introduced in a previous paper as an abstraction of the lattices of ideals in mp-rings and the lattices of ideals in conormal lattices. several properties of m-rings and conormal lattices were generalized to mp-quantales. in this paper we shall prove new characterization theorems for mp-quantales and for semiprime mp-quantales (these last structures coincide with the p f - quantales). some proofs reflect the way in which the reticulation functor (from coherent quantales to bounded distributive lattices) allows us to export some properties from conormal lattices to mp-quantales.