Document Type : Research Paper

Author

Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania.

10.22105/jfea.2021.279892.1090

Abstract

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 PF-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.

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