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

DOI10.1007/S13370-018-0641-XzbMath1449.13003OpenAlexW2903349060WikidataQ128900988 ScholiaQ128900988MaRDI QIDQ2181205

Daouda Sangare

Publication date: 18 May 2020

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-018-0641-x

zbMATH Keywords

Poincaré seriesanalytic spreadmultiplicitiesHilbert functionsgraded rings and modules\(f\)-good filtrationsfunctions of polynomial typeNoetherian filtrationsnon-standard graded ringsquasi-polynomial functions

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Graded rings (13A02) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Formal power series rings (13F25)

Cites Work

• Generalized Samuel numbers and A.P filtrations
• Reductions of filtrations
• Notes on essentially powers filtrations
• Hilbert functions, Hilbert-Samuel quasi-polynomials with respect to \(f\)-good filtrations, multiplicities
• Asymptotic closure of filtrations on rings with Krull dimension 1
• Some asymptotic properties of powers of ideals
• Hilbert–Samuel functions of well bifiltered modules
• Krull dimension and transcendence degree
• Note on i-good filtrations and noetherian rees rings
• Filtrations, Asymptotic and Pruferian Closures, Cancellation Laws
• Filtrations, integral dependence, reduction, f-Good filtrations
• Asymptotic properties of filtrations on a module
• Analytic spread of nitrations, asymptotic nature and some stability properties
• IDENTIFICATION OF THE HILBERT FUNCTION AND POINCARÉ SERIES, AND THE DIMENSION OF MODULES OVER FILTERED RINGS
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