The construction of a universal enveloping algebra of a Lie algebra can be generalized in several ways. One of them is to generalize it to Lie algebroids and, slightly more general, to the Lie-Rinehardt algebra?s. This leads to the universal enveloping algebroids. Some standard theorems like the PBW theorem generalize to some extend to this context.
George S. Rinehart, Differential forms on general commutative algebras, Trans. Amer. Math. Soc. 108 1963 195–222 (MR0154906 (27 #4850))