Freiman Borel type ideals

2022/01/20 by Guangjun Zhu, Yakun Zhao, Zhu, Guangjun +5
Computer Science · Mathematics · #05E40 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13E15 #Secondary 13F20

paper · pdf · doi:10.48550/arxiv.2201.08240

openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

An equigenerated monomial ideal I in the polynomial ring S= K[x₁,…,x_n] is a Freiman ideal if μ(I²)=ℓ(I)μ(I)-ℓ(I)\choose 2 where ℓ(I) is the analytic spread of I and μ(I) is the number of minimal generators of I. In this paper, we classify certain classes of Borel type ideals, including Borel ideals with multiple Borel generators and principal k-Borel ideals, which are Freiman.

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