Dimension de Heitmann des treillis distributifs et des anneaux commutatifs

TL;DR

This paper explores generalized notions of dimension in distributive lattices and spectral spaces, providing constructive proofs of key theorems in commutative algebra and introducing new results.

Contribution

It extends Heitmann's dimension concept to a broader framework, offering simpler, constructive proofs and novel insights in commutative algebra.

Findings

Constructive versions of classical theorems in commutative algebra

Simplified proofs compared to traditional approaches

Introduction of new results in the theory of distributive lattices

Abstract

We study a notion of dimension which was introduced by R. Heitmann in his remarkable paper in 1984, and also a related notion, implicit in the proofs in his paper. We develop these notions in the general framework of distributive lattices and spectral spaces. We obtain in this way constructive versions of important theorems in commutative algebra, with simpler proofs than the classical ones, and some new results.