  Let R be either a polynomial or a formal power series ring in a finite number
of variables over a field k of characteristic p > 0 and let D be the ring of
klinear differential operators of R. In this paper we prove that if f is a
non-zero element of R then R[1/f], obtained from R by inverting f, is generated
as a D-module by 1/f . This is very much in contrast to the characteristic zero
situation where the corresponding statement is false (there the generation is
governed by the roots of the Bernstein polynomial of f). In fact we prove
analogs of the above result for a considerably wider class of rings R and a
considerably wider class of D-modules.
