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We present constructive versions of Krull's dimension theory for commutativerings and distributive lattices. The foundations of these constructive versionsare due to Joyal, Espan\~ol and the authors. We show that this gives aconstructive version of basic classical theorems (dimension of finitelypresented algebras, Going up and Going down theorem, \ldots), and hence that weget an explicit computational content where these abstract results are used toshow the existence of concrete elements. This can be seen as a partialrealisation of Hilbert's program for classical abstract commutative algebra.

Hidden constructions in abstract algebra, Krull Dimension, Going Up, Going Down