The aim of this article is to develop a Priestley-style duality for the variety of DN-algebras. In order to achieve this, we use the concept of free distributive lattice extension of a DN-algebra. We establish a connection with the Priestley duality for distributive lattices. Finally, we present topological descriptions for the lattice of filters, for the lattice of congruences, and for certain kinds of subalgebras of a DN-algebra.

中文翻译：

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DN 代数的 Priestley 式对偶性

本文的目的是为各种 DN 代数开发一种 Priestley 式的对偶性。为了实现这一点，我们使用 DN 代数的自由分配格扩展的概念。我们与分配格的普里斯特利对偶性建立了联系。最后，我们提出了滤波器格、同余格以及 DN 代数的某些类型的子代数的拓扑描述。