Notes on the behavior of the Ratliff-Rush filtration

2002/09/23 by Maria Evelina Rossi, Rossi, Maria Evelina, Irena Swanson +1 · 2 citations
Engineering · Environmental Science · Mathematics · #13A30 #13B22 #13P10 #Commutative Algebra (math.AC) #Dam Engineering and Safety #FOS: Mathematics #Groundwater flow and contamination studies #Hydraulic Fracturing and Reservoir Analysis #math.AC #msc:13A30 #msc:13B22 #msc:13P10

paper · pdf · doi:10.48550/arxiv.math/0209308

arxiv created 2002/09/23 · openalex publication_date 2002/09/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals, associated primes, leading term ideals, and the minimal number of generators. In contrast, the reduction number of the Ratliff-Rush filtration behaves better: it preserves some information on the reduction number of the ideal.

Cited by

• Bounds on the second Hilbert coefficient and the depth of the associated graded ring
• On the Ratliff-Rush closure of an ideal of a one-dimensional ring

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