2003/05/22 by Hans Schoutens, HANS SCHOUTENS · 16 citations
Computer Science · Mathematics · #Affine transformation #Algebra over a field #Closure (psychology) #Combinatorics #Commutative Algebra and Its Applications #Discrete mathematics #Ideal (ethics) #Law #Mathematics #Polynomial and algebraic computation #Prime (order theory) #Pure mathematics #Rings, Modules, and Algebras
paper · doi:10.1142/s0219498803000490
published in Journal of Algebra and Its Applications 02(02), 177-187 (World Scientific)
openalex publication_date 2003/05/22 · crossref created 2003/05/22 · crossref issued 2003/06/01 · crossref published 2003/06/01 · crossref published-print 2003/06/01 · crossref published-online 2011/11/21 · crossref deposited 2019/08/07 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/01
In this paper, an alternative proof is presented of the following result on symbolic powers due to Ein, Lazarsfeld and Smith [3] (for the affine case over [Formula: see text]) and to Hochster and Huneke [4] (for the general case). Let A be a regular ring containing a field K. Let [Formula: see text] be a radical ideal of A and let h be the maximum of the heights of its minimal primes. Then for all n, we have an inclusion [Formula: see text], where the first ideal denotes the hnth symbolic power of [Formula: see text]. In prime characteristic, this result admits an easy tight closure proof due to Hochster and Huneke. In this paper, the characteristic zero version is obtained from this by an application of the Lefschetz Principle.