Primary Decompositions of Regular Sequences

2023/01/05 by Thomas Polstra, Polstra, Thomas
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2301.02285

openalex publication_date 2023/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Noetherian ring and x₁,…,x_t a permutable regular sequence of elements in R. Then there exists a finite set of primes Λ and natural number C so that for all n₁,…,n_t there exists a primary decomposition (x₁^n₁,…,x_t^n_t)=Q₁∩ ⋯ ∩ Q_ℓ so that √(Q_i)∈ Λ and √(Q_i)^{C(n₁+⋯ + n_t)}⊆ Q_i for all 1≤ i≤ ℓ.

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