Quantum de Rham cohomology ring for Poisson manifolds

In [4] we have proved that the quantum de Rham cohomology of a Poisson manifold $(M, \omega)$ (see [1]) can be obtained via deformational quantization of the de Rham cohomology of $M$. In this paper we prove that the ring structure on the quantum cohomology of $(M,\omega)$ is obtained via deformational quantization of the ring structure of de Rham cohomology of $M$.