Growth of Algebras

Abstract

Let A be an F-algebra. We say that A is nitely generated provided there is fa1; a2; ; ar g A such that every element of A can be written as a nite linear combination of monomials in a1; a2; : : : ; ar . V will denote the F-span of fa1; a2; : : : ; ar g. V is called a nite dimensional generating subspace (fdgs) for A.