Hidden constructions in abstract algebra: Krull dimension of distributive lattices and commutative rings
Paper i proceeding, 2003

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.


Thierry Coquand

Göteborgs universitet

Henri Lombardi

Lecture Notes in Pure and Applied Mathematics

0075-8469 (ISSN)

Vol. 231 477-499