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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 2, Pages 19–39 (Mi izv801)  

This article is cited in 2 scientific papers (total in 2 papers)

Indentification of the Hilbert function and Poincaré series, and the dimension of modules over filtered rings

V. V. Bavula


Abstract: In this paper it is shown how to reconstruct a Poincaré series from a known Hilbert (integral) function of a graded module over a commutative Noetherian graded ring, and vice versa. The dimension and multiplicity of modules over a filtered ring whose associated graded ring is commutative and Noetherian are introduced. For one class of generalized Weyl algebras that includes the Weyl algebras $A_n$, the Krull dimension is computed, and Bernstein's inequality is proved and strengthened.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 225–246

Bibliographic databases:

UDC: 512.54
MSC: Primary 16S32; Secondary 16P20, 16P40, 16P60, 16P90, 16W50
Received: 26.03.1992

Citation: V. V. Bavula, “Indentification of the Hilbert function and Poincaré series, and the dimension of modules over filtered rings”, Izv. RAN. Ser. Mat., 58:2 (1994), 19–39; Russian Acad. Sci. Izv. Math., 44:2 (1995), 225–246

Citation in format AMSBIB
\Bibitem{Bav94}
\by V.~V.~Bavula
\paper Indentification of the Hilbert function and Poincar\'e series, and the dimension of modules over filtered rings
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 2
\pages 19--39
\mathnet{http://mi.mathnet.ru/izv801}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1275900}
\zmath{https://zbmath.org/?q=an:0845.16018}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..225B}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 2
\pages 225--246
\crossref{https://doi.org/10.1070/IM1995v044n02ABEH001595}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB41200002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. H. Dichi, D. Sangaré, “Hilbert functions, Hilbert-Samuel quasi-polynomials with respect to ƒ-good filtrations, multiplicities”, Journal of Pure and Applied Algebra, 138:3 (1999), 205  crossref
    2. V. Bavula, F. van Oystaeyen, “Simple Holonomic Modules over the Second Weyl Algebra A2”, Advances in Mathematics, 150:1 (2000), 80  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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