Differential basis and 𝑝-basis of a regular local ring

Abstract

We prove that any differential basis of a regular local ring R R of characteristic p > 0 p > 0 over R p {R^p} is a p p -basis of R R over R p {R^p} . This result gives a characterization of a regular local ring R R which has a p p -basis over R p {R^p} .