Finite algebra
An -algebra is finite if it is finitely generated as an -module. An -algebra can be thought as a homomorphism of rings, in this case is called a finite morphism if is a finite -algebra.
The definition of finite algebra is related to that of algebras of finite type.This concept is closely related to that of finite morphism in algebraic geometry; in the simplest case of affine varieties, given two affine varieties, and a dominant regular map, the induced homomorphism of -algebras defined by turns into a -algebra:
The generalisation to schemes can be found in the article on finite morphisms.
