Sets of Hilbert series and their applications
arXiv:math/0502149
Abstract
There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer , the set of Hilbert series of right-sided ideals with generators and relations of degrees at most in a f. p. algebra is finite. Second, every f. p. module of linear growth over noetherian or coherent algebra has periodic Hilbert function. Third, every ideal in a Koszul family of ideals (defined in math.AG/0412441) in a f. p. algebra has rational Poincare series.
10 pages