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Sets of Hilbert series and their applications

Dmitri Piontkovski
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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 $D$, 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.

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Dmitri Piontkovski. 2005-02-08. Sets of Hilbert series and their applications. https://arxiv.org/abs/math/0502149

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