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Titolo:
Primary ideals with good associated graded ring
Autore:
Rossi, ME;
Indirizzi:
Univ Genoa, Dept Math, I-16146 Genoa, Italy Univ Genoa Genoa Italy I-16146 iv Genoa, Dept Math, I-16146 Genoa, Italy
Titolo Testata:
JOURNAL OF PURE AND APPLIED ALGEBRA
fascicolo: 1, volume: 145, anno: 2000,
pagine: 75 - 90
SICI:
0022-4049(20000105)145:1<75:PIWGAG>2.0.ZU;2-S
Fonte:
ISI
Lingua:
ENG
Soggetto:
MACAULAY LOCAL-RINGS; COHEN-MACAULAY; FORM RINGS; COEFFICIENTS; CONJECTURE; SALLY,J;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
21
Recensione:
Indirizzi per estratti:
Indirizzo: Rossi, ME Univ Genoa, Dept Math, Via Dodecaneso 35, I-16146 Genoa, Italy Univ Genoa Via Dodecaneso 35 Genoa Italy I-16146 6 Genoa, Italy
Citazione:
M.E. Rossi, "Primary ideals with good associated graded ring", J PURE APPL, 145(1), 2000, pp. 75-90

Abstract

Let (A, M) be a local Cohen-Macaulay ring of dimension d. Let I be an, K-primary ideal and let J be the ideal generated by a maximal superficial sequence for I. Under these assumptions Valabrega and Valla (Nogoya Math. J. 72(1978) 93-101) proved that the associated graded ring G of I is Cohen-Macaulay if and only if I-n boolean AND J =JI(n-1) for every integer n. In thispaper we consider the class of the M-primary ideals I such that, for some positive integer k, we have I-n boolean AND J =JI(n-1) for n less than or equal to k and lambda(Ik+1/JI(k)) less than or equal to 1. In this case G need not be Cohen-Macaulay. In Theorem 2.2. we show that G is Cohen-Macaulay unless the ideals we are considering are of maximal Cohen-Macaulay type. One can use the ideas of Rossi and Valla (Comm. Algebra 24(13) (1996) 4249-4261; Pure Appl. Algebra 122 (1997) 293-311) to prove that, for the ideals weconsider, the depth of G is at least d-1 and that its h-vector has no negative components. We characterize the possible Hilbert function of G. Our approach gives proof of an extended version of a conjecture of Sally (proved in Rossi and Valla (Comm. Algebra 24(13) (1996) 4249-4261)) and independently in Wang (J. Algebra 190 (1997) 226-240) in the case I=M). Several results proved in Huckaba (Comm. Algebra, to appear), Rossi and Valla (Nogoya Math. J. 110 (1988) 81-111; Comm. Algebra 24(13) (1996) 4249-4261; J. Pure Appl. Algebra 122 (1997) 293-311) and Sally (J. Algebra 83 (1983) 325-333) areunified and generalized. (C) 2000 Elsevier Science B.V. All rights reserved.

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Documento generato il 24/09/20 alle ore 08:15:59