Abstract
Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the canonical map from the above enveloping algebra to the ring of differential operators DA/k is an isomorphism. This result generalizes the characteristic 0 case in which the ring DA/k appears as the enveloping algebra of the Lie-Rinehart algebra of the usual k-derivations of A provided that A is smooth over k.
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