Let $A$ be any commutative ring with 1. A power series $f\in A[[t]]$ is called rational if we can find a $g\in A[t]$ such that $fg\in A[t]$. It is clear that the set of rational power series forms a ring which I call $R_A$.
I am looking for references giving properties of $R_A$ in terms of properties of $A$. For example is it true that $R_A$ is noetherian if $A$ is noetherian?
If $A$ is a field this should be ok because $R_A=A(t)$ which is a field.
Other properties I would like to know are flatness and integrality of $R_A$.