Fluctuations in depth and associated primes of powers of ideals

2023/09/26 by Roswitha Rissner, Rissner, Roswitha, Irena Swanson +1 · 1 citation
Computer Science · Mathematics · #13A15 (Primary) 13C15 #13F20 (Secondary) #Advanced Mathematical Identities #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2309.15083

openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We count the numbers of associated primes of powers of ideals as defined by Bandari, Hibi, and Herzog in 2014. We generalize those ideals to monomial ideals BHH(m,r,s) for r ≥ 2, m, s ≥ 1; we establish partially the associated primes of powers of these ideals, and we establish completely the depth function of quotients by powers of these ideals: the depth function is periodic of period r repeated m times on the initial interval before settling to a constant value. The number of needed variables for these depth functions are lower than those from general constructions by Hà, Nguyen, Trung, and Trung (2021).

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