Extended curvatures and Lie pseudoalgebras

The aim of the paper is to prove that if some extended curvatures on a preinfinitesimal module L , considered in the paper, vanish, then the derived preinfinitesimal module L (1) is a Lie pseudoalgebra. Two non-trivial examples are given. The first example is when L 0 is an infinitesimal module and the second one is when L 1 is a preinfinitesimal module.