Let $A$ be a ring and $A[[T]]$ the formal power series over $A$. Then, one can show that $\Omega^1_{A[[T]]/A}$ is not finitely generated over $A[[t]]$. Now, in $\Omega^1_{A[[T]]/A}$ I am trying to show that the intersection $\cap_{n \geq 1} T^i \Omega^1_{A[[T]]/A} $ is non-zero in general, and that it can even be non-zero if $A$ is a field of characteristic 0.
I can show that the intersection is non-zero if $A$ is not an integral domain, but if $A$ is a field of characteristic 0, then I don't see how to proceed. Any hints or solutions?
Edit:
Possible directions to consider might be to look at the relation $A[[t]]=A[t]+(t^n)A[[t]]$ for any $n >0$. But once again, I dont' neccesarily see how to construct an element in the intersection directly! Any thoughts are welcome.