  For a Lie-Rinehart algebra (A,L) such that, as an A-module, L is finitely
generated and projective of finite constant rank, the relationship between
generators of the Gerstenhaber bracket and connections on the highest
A-exterior power of L given in an earlier paper arises from the canonical
pairing between the exterior A-powers of L. Thus, given an exact generator for
the corresponding Gerstenhaber algebra, the chain complex underlying the
resulting Batalin-Vilkovisky algebra coincides with the Rinehart complex
computing the corresponding Lie-Rinehart homology.
