The \(D\)-module structure of \(F\)-split rings
type: Item
instance of: scholarly article
title: The \(D\)-module structure of \(F\)-split rings
zbMATH Open document ID: 0848.13010
published in: Mathematical Research Letters
publication date: 1995-11-16T00:00:00Z
review text: Let \(R\) be a reduced Noetherian ring, finitely generated over its subring \(R^p\) of \(p\)-th powers, where \(p = \text{char} (R)\) is prime. Let \(D_A (R)\) \((= D)\) be the ring of \(A \)-linear differential operators of \(R\). Questions of \textit{T. Levasseur} and \textit{J. T. Stafford} [``Rings of differential operators on classical rings of invariants'', Mem. Am. Math. Soc. 412 (1989; Zbl 0691.16019)] motivate the author to make connections between the \(D\)-module structure of \(R\) and the Hochster-Huneke tight closure theory. The results include that \(R\) is strongly \(F\)-regular if and only if \(R\) is \(F\)-split and is a finite product of \(D\)-simple rings.
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13N10
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 817763
zbMATH Keywords: prime characteristic
zbMATH Keywords: \(D\)-module
zbMATH Keywords: differential operators
zbMATH Keywords: tight closure
author: K. E. Smith
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
DOI: 10.4310/MRL.1995.V2.N4.A1
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description: scientific article; zbMATH DE number 817763