In commutative algebra, given a homomorphism of commutative rings, is called an -algebra of finite type if can be finitely generated as an -algebra. It is much stronger for to be a finite -algebra, which means that is finitely generated as an -module. For example, for any commutative ring and natural number , the polynomial ring is an -algebra of finite type, but it is not a finite -algebra unless = 0 or = 0. Another example of a finite-type homomorphism that is not finite is .