IDENTIFICATION OF THE HILBERT FUNCTION AND POINCARÉ SERIES, AND THE DIMENSION OF MODULES OVER FILTERED RINGS

DOI10.1070/IM1995v044n02ABEH001595zbMath0845.16018MaRDI QIDQ4847192

Vladimir V. Bavula

Publication date: 10 September 1995

Published in: Russian Academy of Sciences. Izvestiya Mathematics (Search for Journal in Brave)

zbMATH Keywords

Poincaré seriesgraded modulesKrull dimensiongeneralized Weyl algebrasHilbert functionsfiltered ringscommutative Noetherian graded rings

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Rings of differential operators (associative algebraic aspects) (16S32) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (9)

A partial characterization of Hilbert quasi-polynomials in the non-standard case ⋮ On the asymptotic behaviour of Hilbert functions of graded rings and modules: applications to the Hilbert-Samuel functions of well filtered modules, multiplicity and analytic spread of nice filtrations ⋮ Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2 ⋮ Simple holonomic modules over the second Weyl algebra \(A_2\) ⋮ Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic ⋮ Filter Dimension ⋮ On projective modules over quantum polynomials ⋮ Hilbert functions, Hilbert-Samuel quasi-polynomials with respect to \(f\)-good filtrations, multiplicities ⋮ Holonomic modules for rings of invariant differential operators

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