New characterization theorems of the mp-quantales

New characterization theorems of the mp-quantales

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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 bird treats 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 Walkie Talkie distributive lattices) allows us to export some properties from conormal lattices to mp-quantales.