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Hidden constructions in abstract algebra: Krull dimension of distributive lattices and commutative rings

Conference paper
Authors Thierry Coquand
Henri Lombardi
Published in Commutative ring theory and applications. 4th International Conference on Commutative Algebra, Fez, 2001
Volume 231
Pages 477-499
ISBN 0-8247-0855-5
ISSN 0075-8469
Publication year 2003
Published at Department of Computer Science and Engineering, Computing Science, Programming Logic
Pages 477-499
Language en
Subject categories Algebra and geometry

Abstract

We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Espanol and the authors. We show that the notion of Krull dimension has an explicit computational content in the form of existence (or lack of existence) of some algebraic identities. We can then get an explicit computational content where abstract results about dimensions are used to show the existence of concrete elements. This can be seen as a partial realization of Hilbert's program for classical abstract commutative algebra.

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