Bounds on the a-invariant and reduction numbers of ideals

D'Cruz, Clare ; Kodiyalam, Vijay ; Verma, J. K. (2004) Bounds on the a-invariant and reduction numbers of ideals Journal of Algebra, 274 (2). pp. 594-601. ISSN 0021-8693

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Let R be a d-dimensional standard graded ring over an Artinian local ring. Let M be the unique maximal homogeneous ideal of R. Let hi(R)n denote the length of the nth graded component of the local cohomology module HiM(R). Define the Eisenbud–Goto invariant EG(R) of R to be the number Σq=0d-1d-1qhqM(R)1-q. We prove that the a-invariant a(R) of the top local cohomology module HMd satisfies the inequality: a(R)⩽e(R)−ℓ(R1)+(d−1)(ℓ(R0)−1)+EG(R). This bound is used to get upper bounds for the reduction number of an -primary ideal I of a Cohen–Macaulay local ring (R,m), when the associated graded ring of I has depth at least d−1.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:a-Invariant; Reduction Number; Eisenbud–goto Invariant; Local Cohomology
ID Code:109065
Deposited On:25 Oct 2017 13:11
Last Modified:25 Oct 2017 13:11

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