Ratliff-Rush ideal and reduction numbers

2015/10/08 by Mafi, Amir
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.02278

Abstract

Let (R,m) be a Cohen-Macaulay local ring of positive dimension d and infinite residue field. Let I be an m-primary ideal and J a minimal reduction of I. In this paper, we show that \widetilder_J(I)≤ r_J(I). This answer to a question that made by M.E. Rossi and I. Swanson in [\refRs, Question 4.6].

Related

• On the computation of the Ratliff-Rush closure, associated graded ring\n and invariance of a length
• On the computation of Ratliff-Rush closure
• A note on Ratliff-Rush filtration, reduction number and postulation number of \mathfrak m-primary ideals
• Bounds on the Castelnuovo-Mumford Regularity in dimension two
• Results on the Hilbert coefficients and reduction numbers