 
Summary: GENERATORS OF DMODULES IN POSITIVE
CHARACTERISTIC
JOSEP ALVAREZMONTANER, MANUEL BLICKLE, AND GENNADY LYUBEZNIK
Abstract. Let R = k[x1, . . . , xd] or R = k[[x1, . . . , xd]] 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 DRk be the ring of k
linear differential operators of R. In this paper we prove that if f is
a nonzero element of R then Rf , obtained from R by inverting f, is
generated as a DRkmodule by 1
f
. This is an amazing fact considering
that the corresponding characteristic zero statement is very false. In
fact we prove an analog of this result for a considerably wider class of
rings R and a considerably wider class of DRkmodules.
1. Introduction
Let k be a field and let R = k[x1, . . . , xd], or R = k[[x1, . . . , xd]] be either
a ring of polynomials or formal power series in a finite number of variables
over k. Let DRk be the ring of klinear differential operators on R. For
every f R, the natural action of DRk on R extends uniquely to an action
on the localization Rf via the standard quotient rule. Hence Rf acquires
