2022/07/29 by Daniel Smolkin
Mathematics · #Algebraic structures and combinatorial models #Class (philosophy) #Combinatorics #Commutative Algebra and Its Applications #Diagonal #Discrete mathematics #Field (mathematics) #Finite field #Geometry #Ideal (ethics) #Law #Mathematics #Maximal ideal #Prime (order theory) #Pure mathematics #Ring (chemistry) #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A15 #msc:13A35 #msc:14B05
paper · pdf · doi:10.46298/epiga.2023.9918
published as Épijournal de Géométrie Algébrique, Volume 8 (January 22, 2024) epiga:9918 · Copy edited and formatted in the EpiGA journal's stylesheet
arxiv created 2024/01/19 · openalex publication_date 2024/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21 · arxiv updated 2026/08/05
Let J be any ideal in a strongly F-regular, diagonally F-split ring R essentially of finite type over an F-finite field. We show that Js+t ⊆ τ(Js - ε) τ(Jt-ε) for all s, t, ε > 0 for which the formula makes sense. We use this to show a number of novel containments between symbolic and ordinary powers of prime ideals in this setting, which includes all determinantal rings and a large class of toric rings in positive characteristic. In particular, we show that P(2hn) ⊆ Pn for all prime ideals P of height h in such rings. Comment: Copy edited and formatted in the EpiGA journal's stylesheet