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Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters

Published online by Cambridge University Press:  11 January 2016

Shiro Goto  and
Kazuho Ozeki
Shiro Goto
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, goto@math.meiji.ac.jp
Kazuho Ozeki
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, kozeki@math.meiji.ac.jp
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Abstract

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Let (A,m) be a Noetherian local ring with d = dim A ≥ 2. Then, if A is a Buchsbaum ring, the first Hilbert coefficients of A for parameter ideals Q are constant and equal to where hi(A) denotes the length of the ith local cohomology module 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 are constant, which are independent of the choice of parameter ideals Q in A. Hence, a conjecture raised by [GhGHOPV] is settled affirmatively.

Keywords

13H1013A3013B2213H15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 199 , September 2010 , pp. 95 - 105
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

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