The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence P 0 ⊊ ⊊ P 1 ⊊ ⊊ ⋯ ⋯ ⊊ ⊊ P n 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.