There arc some inequalities concerning the module o] derivations o] a local ring which are tm~e in characteristic 0 and ]alse in general i~a characteristic p =fi 0 (as it is well known) ; in the present paper we prove that such inequalities in char. p are true ]or the module o] iutegrable derivations. Moreover we give some suNicient conditions for an associated prime ideal to be di]#rentiable in char. p.
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