Reticulation of a quantale, pure elements and new transfer properties

We know from a previous paper that the reticulation of coherent quantale A is bounded distributive lattice L ( ) whose prime spectrum homeomorphic to m -prime . This studies how can be used for transferring some properties lattices quantales and vice versa. shall illustrate this thesis by proving several results on pure w –pure elements means In particular, we investigate σ –ideals transferred Then obtained transfer are prove new algebraic topological characterization theorems important classes quantales: normal quantales, mp –quantales, PF purified PP –quantales.