Domains with linear growth (Q1326947)

Let \(A\) be an affine \(k\)-algebra, \(k\) a field, and \(V\) a finite dimensional \(k\)-subspace of \(A\) that contains 1 and a set of generators of \(A\). The ``growth'' of \(A\) (relative to \(V\)) is said to be bounded by a linear polynomial if there exists a constant \(c\) such that \(f(n) \leq cn\) for all \(n\). In the paper it is shown that an affine \(k\)-algebra \(R\) that is a domain with growth bounded by a linear polynomial satisfies a polynomial identity and hence is a finite module over its center.