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September 2010 Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters
Shiro Goto, Kazuho Ozeki
Nagoya Math. J. 199: 95-105 (September 2010). DOI: 10.1215/00277630-2010-004

Abstract

Let Am be a Noetherian local ring with d=dimA2. Then, if A is a Buchsbaum ring, the first Hilbert coefficients eQ1A of A for parameter ideals Q are constant and equal to -i=1d-1d-2i-1hiA, where hiA denotes the length of the ith local cohomology module HmiA of A with respect to the maximal ideal m. This paper studies the question of whether the converse of the assertion holds true, and proves that A is a Buchsbaum ring if A is unmixed and the values eQ1A are constant, which are independent of the choice of parameter ideals Q in A. Hence, a conjecture raised by [GhGHOPV] is settled affirmatively.

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Shiro Goto. Kazuho Ozeki. "Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters." Nagoya Math. J. 199 95 - 105, September 2010. https://doi.org/10.1215/00277630-2010-004

Information

Published: September 2010
First available in Project Euclid: 14 September 2010

zbMATH: 1210.13021
MathSciNet: MR2730412
Digital Object Identifier: 10.1215/00277630-2010-004

Subjects:
Primary: 13H10
Secondary: 13A30, 13B22, 13H15

Rights: Copyright © 2010 Editorial Board, Nagoya Mathematical Journal

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