The \(D\)-module structure of \(F\)-split rings
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.
scientific article; zbMATH DE number 817763