Sets of Hilbert series and their applications

2005/02/08 by Dmitri Piontkovski, Piontkovski, Dmitri
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.RA #msc:16P90 #msc:16W50

paper · pdf · doi:10.48550/arxiv.math/0502149

10 pages

arxiv created 2005/02/08 · arxiv updated 2009/12/01

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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