Hilbert-Samuel function and Grothendieck group
2000 ◽
Vol 43
(1)
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pp. 73-94
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AbstractLet (A, m) be a Noetherian local ring such that the residue field A/m is infinite. Let I be arbitrary ideal in A, and M a finitely generated A-module. We denote by ℓ(I, M) the Krull dimension of the graded module ⊕n≥0InM/mInM over the associated graded ring of I. Notice that ℓ(I, A) is just the analytic spread of I. In this paper, we define, for 0 ≤ i ≤ ℓ = ℓ(I, M), certain elements ei(I, M) in the Grothendieck group K0(A/I) that suitably generalize the notion of the coefficients of Hilbert polynomial for m-primary ideals. In particular, we show that the top term eℓ (I, M), which is denoted by eI(M), enjoys the same properties as the ordinary multiplicity of M with respect to an m-primary ideal.
2013 ◽
Vol 212
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pp. 97-138
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2009 ◽
Vol 61
(4)
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pp. 762-778
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1992 ◽
Vol 111
(1)
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pp. 47-56
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Keyword(s):
2016 ◽
Vol 16
(09)
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pp. 1750163
Keyword(s):
2009 ◽
Vol 37
(5)
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pp. 1594-1603
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