The index of reducibility of parameter ideals in low dimension

2004/08/11 by Mark W. Rogers, Mark Rogers, Rogers, Mark W.
Computer Science · Mathematics · #13D45 (Secondary) #13H10 (Primary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13D45 #msc:13H10

paper · pdf · doi:10.48550/arxiv.math/0408143

12 pages. J. Algebra 278/2 (2004) 571-584 (to appear)

arxiv created 2004/08/11 · openalex publication_date 2004/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Results are presented concerning the following question: If M is a finitely-generated module with finite local cohomologies over a Noetherian local ring (A, m), does there exist an integer n such that every parameter ideal for M contained in mⁿ has the same index of reducibility? We show that the answer is yes if M has dimension 1 or if M has dimension 2 and positive depth. 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.

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