Ratliff¿Rush filtration, regularity and depth of higher associated graded modules: Part I

By Tony J. Puthenpurakal. 2004

50 citations recorded by the source corpus.

Abstract In this paper we introduce a new technique to study associated graded modules. Let ( A , m ) be a Noetherian local ring with depth A ≥ 2 . Our techniques give a necessary and sufficient condition for depth G m n ( A ) ≥ 2 for all n ≫ 0 . Other applications are also included; most notable is an upper bound regarding the Ratliff–Rush filtration.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f962b54900a3f4428ef3842aba1e58e1bd636b4c

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In Algebra and Number Theory

1. G. Valla
2. M. Rossi

In Geometry and Topology

1. M. Rossi
2. G. Valla

Citations in the corpus

• Hilbert Functions of Filtered Modules (2007, background): “The second statement in Theorem 2 of [68] says that if M = A is CohenMacaulay, q = m, dimA = 2 and e1(A) = 2e0(A) − μ(m) + 1, then either grmn(A) is Cohen-Macaulay for n ≫ 0 or depth grm(A) ≥ 1.”