2005/01/28 by Mordechai Katzman, Katzman, Mordechai, Rodney Y. Sharp +1 · 1 citation
Computer Science · Mathematics · #13A15 #13A35 #13E05 #13H10 #16S36 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13A15 #msc:13A35 #msc:13E05 #msc:13H10 #msc:16S36
paper · pdf · doi:10.48550/arxiv.math/0501501
Accepted for publication in the Journal of Algebra
arxiv created 2005/01/28 · openalex publication_date 2005/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with ideals in a commutative Noetherian ring R of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of R generated by regular sequences exhibit a desirable type of `uniform' behaviour. The principal technical tool used is a result, proved by R. Hartshorne and R. Speiser in the case where R is local and contains its residue field which is perfect, and subsequently extended to all local rings of prime characteristic by G. Lyubeznik, about a left module over the skew polynomial ring R[x,f] (associated to R and the Frobenius homomorphism f, in the indeterminate x) that is both x-torsion and Artinian over R.