Editing Dimension (section)

===Krull dimension===
The [[Krull dimension]] of a [[commutative ring]] is the maximal length of chains of [[prime ideal]]s in it, a chain of length ''n'' being a sequence <math>\mathcal{P}_0\subsetneq \mathcal{P}_1\subsetneq \cdots \subsetneq\mathcal{P}_n </math> of prime ideals related by inclusion. It is strongly related to the dimension of an algebraic variety, because of the natural correspondence between sub-varieties and prime ideals of the ring of the polynomials on the variety.

For an [[algebra over a field]], the dimension as [[vector space]] is finite if and only if its Krull dimension is 0.