Modules of differentials in characteristic \(p\) (Q1116989)

The aim of this paper is to give a necessary and sufficient condition for a local noetherian ring \(A\) containing a field \(k\) of characteristic \(p>0\) to have a flat absolute module of differentials; if \(A\) is a Nagata ring the condition is that the morphism \(A^ p\to A\) is flat and with so called ``elementary fibre''. This is an analogue in positive characteristic of a theorem of N. Radu treating the characteristic zero case.