Ratliff-Rush Filtration, regularity and depth of Higher Associated graded modules: Part II

2008/08/24 by Tony J. Puthenpurakal, Puthenpurakal, Tony J. · 2 citations
Mathematics · Medicine · #13A30 #13D40 #13D45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.0808.3258

openalex publication_date 2008/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (A,\m) be a Noetherian local ring, let M be a finitely generated \CM A-module of dimension r ≥ 2 and let I be an ideal of definition for M. Set L^I(M) = \bigoplus_{n≥ 0}M/Iⁿ⁺¹M. In part one of this paper we showed that L^I(M) is a module over \R, the Rees algebra of I and we gave many applications of L^I(M) to study the associated graded module, G_I(M). In this paper we give many further applications of our technique; most notable is a reformulation of a classical result due to Narita in terms of the Ratliff-Rush filtration. This reformulation can be extended to all dimensions ≥ 2.

Cited by

• Quasi-Hilbert rings and Ratliff-Rush filtrations
• Bounds on the second Hilbert coefficient and the depth of the associated graded ring

Related

• Ratliff-Rush Filtration, Regularity and depth of Higher Associated graded modules: Part I
• Ratliff-Rush Filtrations associated with ideals and modules over a Noetherian ring
• The second Hilbert coefficient of modules with almost maximal depth
• Regularity and linearity defect of modules over local rings
• A note on Ratliff-Rush filtration, reduction number and postulation number of \mathfrak m-primary ideals