V. E. Govorov, “On the dimension of graded algebras”, Mat. Zametki, 14:2 (1973), 209–216; Math. Notes, 14:2 (1973), 678

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Matematicheskie Zametki, 1973, Volume 14, Issue 2, Pages 209–216 (Mi mzm7250)

This article is cited in 9 scientific papers (total in 9 papers)

On the dimension of graded algebras

V. E. Govorov

Moscow Institute of Electronic Engineering

Full-text PDF (589 kB) Citations (9)

Abstract: To each graded algebra

R

$R$ with a finite number of generators we associate the series

T (R, z) = \sum d_{n} z^{n}

$T(R,z)=\sum d_nz^n$ , where

d_{n}

$d_n$ is the dimension of the homogeneous component of

R

$R$ . It is proved that if the dimensions

d_{n}

$d_n$ have polynomial growth, then the Krull dimension of

R

$R$ cannot exceed the order of the pole of the series

T (R, z)

$T(R,z)$ for

z = 1

$z=1$ by more than 1.

Received: 03.01.1972

English version:
Mathematical Notes, 1973, Volume 14, Issue 2, Pages 678–682
DOI: https://doi.org/10.1007/BF01147113

Bibliographic databases:

UDC: 512

Language: Russian

Citation: V. E. Govorov, “On the dimension of graded algebras”, Mat. Zametki, 14:2 (1973), 209–216; Math. Notes, 14:2 (1973), 678–682

Citation in format AMSBIB

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\by V.~E.~Govorov

\paper On the dimension of graded algebras

\jour Mat. Zametki

\yr 1973

\vol 14

\issue 2

\pages 209--216

\mathnet{http://mi.mathnet.ru/mzm7250}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=332876}

\zmath{https://zbmath.org/?q=an:0277.16016}

\transl

\jour Math. Notes

\yr 1973

\vol 14

\issue 2

\pages 678--682

\crossref{https://doi.org/10.1007/BF01147113}

Linking options:

https://www.mathnet.ru/eng/mzm7250

https://www.mathnet.ru/eng/mzm/v14/i2/p209

This publication is cited in the following 9 articles:

D. I. Piontkovskii, “Koszul Algebras and Their Ideals”, Funct. Anal. Appl., 39:2 (2005), 120–130
D. I. Piontkovskii, “On the Hilbert Series of Koszul Algebras”, Funct. Anal. Appl., 35:2 (2001), 133–137
Li-Chuan Sun, “Growth of Betti numbers of modules over local rings of small embedding codimension or small linkage number”, Journal of Pure and Applied Algebra, 96:1 (1994), 57
V. A. Ufnarovskii, “On the use of graphs for computing a basis, growth and Hilbert series of associative algebras”, Math. USSR-Sb., 68:2 (1991), 417–428
David J. Anick, Lecture Notes in Mathematics, 1318, Algebraic Topology Rational Homotopy, 1988, 1
I. K. Babenko, “Problems of growth and rationality in algebra and topology”, Russian Math. Surveys, 41:2 (1986), 117–175
David Anick, Clas Löfwall, Lecture Notes in Mathematics, 1183, Algebra, Algebraic Topology and their Interactions, 1986, 32
David J Anick, “Non-commutative graded algebras and their Hilbert series”, Journal of Algebra, 78:1 (1982), 120
James B Shearer, “A graded algebra with a non-rational Hilbert series”, Journal of Algebra, 62:1 (1980), 228

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

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