Infinite power series with unique factorization possible?

Question

Q: Is it possible to define a space of power series over $\mathbb{Q}$ with unique factorization?

It is known that this is possible over $\mathbb{Z}_p$

converging power series over $p$-adic integers is a UFD

Answer 1

For any field $K$, the ring of power series $R_m=K[[x_1,\ldots,x_m]]$ is a UFD. We can prove this by induction:

Prove that the ring of formal power series over a field is an UFD