The Zariski topology for distributive lattices

Abstract

Our purpose in this paper is to study an intrinsic topology for distributive lattices which by its very definition is analogous to the classical Zariski topology on rings. As in the case of rings, the Zariski topology is the coarsest topology making solution sets of polynomials closed. In other words, the Zariski closed sets are generated from a subbase consisting of all sets of the form {z ∈ L: p(z) — c} where p(x) is a polynomial over L and c is an arbitrary but element from L. © 1987 Rocky Mountain Mathematics Consortium.