The index of reducibility of parameter ideals in low dimension

Abstract

In this paper we present results concerning the following question: if M is a finitely-generated module with finite local cohomologies over a Noetherian local ring , does there exist an integer ℓ such that every parameter ideal for M contained in has the same index of reducibility? We show that the answer is yes if dimM=1 or if dimM=2 and depthM &>0. This research is closely related to work of Goto–Suzuki and Goto-Sakurai; Goto-Sakurai have supplied an answer of yes in case M is Buchsbaum.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jalgebra.2004.02.035

Publication Date

2004

Journal Title

Journal of Algebra

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