  In this paper we introduce two classes of Poisson brackets on algebras (or on
sheaves of algebras). We call them locally free and nonsingular Poisson
brackets. Using the Fedosov's method we prove that any locally free nonsingular
Poisson bracket can be quantized. In particular, it follows from this that all
Poisson brackets on an arbitrary field of characteristic zero can be quantized.
The well known theorem about the quantization of nondegenerate Poisson brackets
on smooth manifolds follows from the main result of this paper as well.
