Hilbert Function and Dimension

Gert-Martin Greuel () and Gerhard Pfister ()
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Gert-Martin Greuel: University of Kaiserslautern, Department of Mathematics
Gerhard Pfister: University of Kaiserslautern, Department of Mathematics

Chapter 5 in A Singular Introduction to Commutative Algebra, 2002, pp 275-312 from Springer

Abstract: Abstract The Hilbert function of a graded module associates to an integer n the dimension of the n-th graded part of the given module. For sufficiently large n, the values of this function are given by a polynomial, the Hilbert polynomial. To show this, we use the Hilbert-Poincaré series, a formal power series in t with coefficients being the values of the Hilbert function. This power series turns out to be a rational function.

Keywords: Prime Ideal; Local Ring; Hilbert Series; Noetherian Ring; Singular Locus (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-662-04963-1_5

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