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Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters
Published online by Cambridge University Press: 11 January 2016
Abstract
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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2010
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