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Some Improvements of a Lemma of Rosenfeld

We give some improvements of a lemma of Rosenfeld which permit us to optimize some algorithms in diierential algebra: we prove the lemma with weaker hypotheses and we demonstrate an analogue of Buchberger's second criterion, which avoids non necessary reductions for detecting coherent sets of diierential polynomials. We try also to clarify the relations between the theorems in diierential algebra and some more widely known results in the Grr obner bases theory.berger's criteria. Polynomial diierential equations. Rosen-feld's lemma.