The Hilbert series of prime PI rings. (Q1885583)

Let \(A\) be an algebra generated over a field \(k\) by a finite dimensional vector space \(V\) with \(1\in V\). The Hilbert series of \(A\) with respect to \(V\) is defined as \(1+\sum_{n\geq 1}\dim(V^n/V^{n-1})t^n\). The main result of the paper under review is that if \(A\) is a finitely generated prime PI-algebra, then its Hilbert series is rational for a suitable generating subspace. Together with the theory of PI-algebras, the proof uses ideas from the theory of noncommutative Gröbner bases.