Bounds for the reduction number of primary ideal in dimension three

2022/09/27 by Mandal, Mousumi, Saloni, Kumari · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.13319

Abstract

Let (R,\mathfrakm) be a Cohen-Macaulay local ring of dimension d≥ 3 and I an \mathfrakm-primary ideal of R. Let r_J(I) be the reduction number of I with respect to a minimal reduction J of I. Suppose depth G(I)≥ d-3. We prove that r_J(I)≤ e₁(I)-e₀(I)+λ(R/I)+1+(e₂(I)-1)e₂(I)-e₃(I), where e_i(I) are Hilbert coefficients. Suppose d=3 and depth G(I^t)>0 for some t≥ 1. Then we prove that r_J(I)≤ e₁(I)-e₀(I)+λ(R/I)+t.

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