On constructing deformations of noncommutative algebras

We show that if there is a flat deformation from a finite-dimensional algebra N to an algebra A, then such a deformation can be obtained by a slight generalization of the construction from [2]. The generalization allows negative powers of t to occur in the formula for f. The proof uses a result from [19].
We also prove that this modified construction produces well-defined formal deformations that are flat deformations from N to A.