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

我们从之前的论文中知道，相干量子A的网状结构是有界分布格$\mathrm{大号}(\mathrm{一个})$其素数谱同胚于A的m素数谱。本文研究了如何使用网状结构将有界分布格的某些性质传递给量子，反之亦然。我们将通过网状化证明量子A的纯元素和w纯元素的几个结果来说明这个论点$\mathrm{大号}(\mathrm{一个})$. 特别是，我们将研究σ -ideals 的性质如何$\mathrm{大号}(\mathrm{一个})$可以转移到A 的纯元素和w纯元素。然后用得到的传递性质证明了一些重要类量子的新的代数和拓扑结果和表征定理：正常量子、mp-量子、PF-量子、纯量子和PP-量子。