Journal of the Mathematical Society of Japan

The reduction exponent of socle ideals associated to parameter ideals in a Buchsbaum local ring of multiplicity two

Shiro GOTO and Hideto SAKURAI

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Abstract

Let A be a Buchsbaum local ring with the maximal ideal m and let e(A) denote the multiplicity of A. Let Q be a parameter ideal in A and put I=Q : m. Then the equality I2=QI holds true, if e(A)=2 and depthA>0. The assertion is no longer true, unless e(A)=2. Counterexamples are given.

Article information

Source
J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1157-1168.

Dates
First available in Project Euclid: 27 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1190905453

Digital Object Identifier
doi:10.2969/jmsj/1190905453

Mathematical Reviews number (MathSciNet)
MR2092942

Zentralblatt MATH identifier
1102.13003

Subjects
Primary: 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Keywords
Buchsbaum ring generalized Cohen-Macaulay ring Cohen-Macaulay ring Gorenstein ring Cohen-Macaulay tyPe local cohomology multiplicity

Citation

GOTO, Shiro; SAKURAI, Hideto. The reduction exponent of socle ideals associated to parameter ideals in a Buchsbaum local ring of multiplicity two. J. Math. Soc. Japan 56 (2004), no. 4, 1157--1168. doi:10.2969/jmsj/1190905453. https://projecteuclid.org/euclid.jmsj/1190905453


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