The saturation number of monomial ideals

2022/11/20 by Reza Abdolmaleki, Abdolmaleki, Reza, Ali Akbar Yazdan Pour +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary: 13F20 #Secondary: 05E40

paper · pdf · doi:10.48550/arxiv.2211.10982

openalex publication_date 2022/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S=\mathbbK[x₁,…, x_n] be the polynomial ring over a field \mathbbK and \mathfrakm= (x₁, …, x_n) be the irredundant maximal ideal of S. For an ideal I ⊂ S, let sat(I) be the minimum number k for which I \colon \mathfrakm^k = I \colon \mathfrakm^k+1. In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables.

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