Gerstenhaber deformation

Definition
Let $$A$$ be an algebra (not necessarily associative) over a field $$k$$. Then, a Gerstenhaber deformation of $$A$$ is defined as an algebra $$\tilde{A}$$ over the ring $$K\nu$$ (ring of formal power series in the formal variable $$\nu$$), such that $$\tilde{A}/\nu\tilde{A} \simeq A$$. Two Gerstenhaber deformations are termed equivalent if they are isomorphic over $$K\nu$$ and a Gerstenhaber deformation is trivial if it is obtained by extending the base ring from $$K$$ to $$K\nu$$.