2023/12/28 by Clay Adams, Francesca Cantor, Adams, Clay +10
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2312.17391
openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reinterpret various properties of Noetherian local rings via the existence of some n-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized Cohen-Macaulayness, and F-purity, among others. Our proofs that such numerical functions exist are nonconstructive and rely on the transference of the property in question from a local ring to its ultrapower or catapower.