Sets of Hilbert series and their applications |
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Authors: | D I Piontkovski |
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Institution: | (1) Central Institute of Economics and Mathematics, Nakhimovsky prosp. 47, Moscow, 117418, Russia |
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Abstract: | We consider graded finitely presented algebras and modules over a field. Under some restrictions, the set of Hilbert series
of such algebras (or modules) becomes finite. Claims of that type imply the rationality of Hilbert and Poincaré series of
some algebras and modules, including the periodicity of Hilbert functions of many (e.g., Noetherian) modules and algebras
of linear growth.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 143–156, 2004. |
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Keywords: | |
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