Dimension theory

Summary

Dimension theory is the part of commutative algebra that studies the Krull dimension of rings and modules. It also studies related notions such as height, system of parameters and multiplicity. Its central results are Krull's principal ideal theorem and the dimension theorem for local rings. The latter computes the Krull dimension of a Noetherian local ring from its Hilbert–Samuel function. It gives an algebraic meaning to the dimension of an algebraic variety.