Let $P$ be a prime ideal in a commutative ring $R$ with unity such that an ideal $Q$ is $P$-primary and some power of $P$ is a subset of $Q$. I want to show that $\sqrt {Q[[x]]}=P[[x]]$.
If a power series $f=a_0+a_1x+a_2x^2+\cdots$ is in $\sqrt {Q[[x]]}$ then some power $f^k$ is in $Q[[x]]$ so that $a_0^k$ belongs to $Q$ whence, by the hypothesis, $a_0$ would be in $P$. But for the other coefficients $a_i$ I could not reach the same result. Thanks for any help!