  There are several remarks on Hilbert series of finitely presented (f. p.)
associative algebras over a field and their modules. First, given an integer
$D$, the set of Hilbert series of right-sided ideals with generators and
relations of degrees at most $D$ 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.
