Ideals of reduction number two

2019/11/20 by Shinya Kumashiro, Kumashiro, Shinya
Computer Science · Mathematics · #13A30 #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1911.08918

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a local Cohen-Macaulay ring (A, m), we study the Hilbert function of an m-primary ideal I whose reduction number is two. It is a continuous work of the papers of Huneke, Ooishi, Sally, and Goto-Nishida-Ozeki. With some conditions, we show the inequality e₁(I)≥ e₀(I) - ℓ_A (A/I) + e₂(I) of the Hilbert coefficients, which is the converse inequality of Sally and Itoh. We also study relations between the Hilbert coefficients and the depth of the associated graded ring.

Related

• Integrally closed ideals of reduction number three
• Results on the Hilbert coefficients and reduction numbers
• Hilbert Coefficients and Depth of the Associated Graded Ring of an Ideal
• The second Hilbert coefficients and the sectional genera of ideals
• Bounds for the reduction number of primary ideal in dimension three