Nagoya Mathematical Journal

Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters

Shiro Goto and Kazuho Ozeki

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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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Nagoya Math. J., Volume 199 (2010), 95-105.

First available in Project Euclid: 14 September 2010

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Zentralblatt MATH identifier

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 13H15: Multiplicity theory and related topics [See also 14C17]


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

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