Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 199 (2010), 95-105.
Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters
Let be a Noetherian local ring with . Then, if is a Buchsbaum ring, the first Hilbert coefficients of for parameter ideals are constant and equal to , where denotes the length of the ith local cohomology module of with respect to the maximal ideal . This paper studies the question of whether the converse of the assertion holds true, and proves that is a Buchsbaum ring if is unmixed and the values are constant, which are independent of the choice of parameter ideals in . Hence, a conjecture raised by [GhGHOPV] is settled affirmatively.
Nagoya Math. J., Volume 199 (2010), 95-105.
First available in Project Euclid: 14 September 2010
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.nmj/1284471571