| has gloss | eng: In mathematics, a finitely generated algebra is an associative algebra A over a field K such that every element of A can be expressed as a polynomial in a finite set of elements a1,…,an of A, with coefficients in K. If it is necessary to emphasize the field K then the algebra is said to be finitely generated over K . Algebras that are not finitely generated are called infinitely generated. Finitely generated commutative algebras are basic objects of consideration in modern algebraic geometry, where they correspond to affine algebraic varieties; for this reason, these algebras are also referred to as (commutative) affine algebras. |