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Titolo:
A bound on the reduction number of a primary ideal
Autore:
Rossi, ME;
Indirizzi:
Univ Genoa, Dipartimento Matemat, I-16146 Genoa, Italy Univ Genoa Genoa Italy I-16146 ipartimento Matemat, I-16146 Genoa, Italy
Titolo Testata:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
fascicolo: 5, volume: 128, anno: 2000,
pagine: 1325 - 1332
SICI:
0002-9939(2000)128:5<1325:ABOTRN>2.0.ZU;2-L
Fonte:
ISI
Lingua:
ENG
Soggetto:
HILBERT COEFFICIENTS; COHEN-MACAULAY; GRADED RINGS;
Keywords:
Cohen-Macaulay local ring; primary ideals; reduction number; minimal reduction; associated graded ring; Hilbert function; Hilbert coefficients;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
20
Recensione:
Indirizzi per estratti:
Indirizzo: Rossi, ME Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy Univ Genoa Via Dodecaneso 35 Genoa Italy I-16146 6 Genoa, Italy
Citazione:
M.E. Rossi, "A bound on the reduction number of a primary ideal", P AM MATH S, 128(5), 2000, pp. 1325-1332

Abstract

Let (A; M) be a local ring of positive dimension d and let I be an M-primary ideal. We denote the reduction number of I by r(I), which is the smallest integer r such that Ir+1 = JI(r) for some reduction J of I: In this paperwe give an upper bound on r(I) in terms of numerical invariants which are related with the Hilbert coefficients of I when A is Cohen-Macaulay. If d =1, it is known that r(I) less than or equal to e(I) 1 where e(I) denotes the multiplicity of I: If d less than or equal to 2; in Corollary 1.5 we prove r(I) less than or equal to e(1)(I) e(I) +lambda(A/I) +1 where e1(I) is the first Hilbert coefficient of I: From this bound several results follow. Theorem 1.3 gives an upper bound on r(I) in a more general setting.

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Documento generato il 19/09/20 alle ore 15:25:55