  In this paper we revisit Ribenboim's notion of higher derivations of modules
and relate it to the recent work of De Fernex and Docampo on the sheaf of
differentials of the arc space. In particular, we derive their formula for the
K\"ahler differentials of the Hasse-Schmidt algebra as a consequence of the
fact that the Hasse-Schmidt algebra functors commute.

Commutative Algebra;Algebraic Geometry;Representation Theory