Reticulation of a quantale, pure elements and new transfer properties

2020/06/14 by Georgescu, George
#FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2006.07829

Abstract

We know from a previous paper that the reticulation of a coherent quantale A is a bounded distributive lattice L(A) whose prime spectrum is homeomorphic to m - prime spectrum of A. In this paper we shall prove several results on the pure elements of the quantale A by means of the reticulation L(A). We shall investigate how the properties of σ - ideals of L(A) can be transferred to pure elements of A. Then the pure elements of A are used to obtain new properties and characterization theorems for some important classes of quantales: normal quantales, mp - quantales, PF - quantales, purified quantales and PP - quantales.

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