On the set of associated radicals of powers of monomial ideals

2024/12/19 by Nguyen Thu Hang, Hang, Nguyen Thu, Trương Thị Hiên +1
Mathematics · #13A15 #13C13 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2412.14904

openalex publication_date 2024/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be a monomial ideal in a polynomial ring. In this paper, we study the asymptotic behavior of the set of associated radical ideals of the (symbolic) powers of I. We show that both \asr(I^s) and \asr(I^(s)) need not stabilize for large value of s. In the case I is a square-free monomial ideal, we prove that \asr(I^(s)) is constant for s large enough. Finally, if I is the cover ideal of a balanced hypergraph, then \asr(I^s) monotonically increases in s.

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