TITLE: What is the fraction field of $R[[x]]$, the power series over some integral domain?
QUESTION [10 upvotes]: I have a question similar to 74335.

Let $R$ be an integral domain. Is there a nice description of the fraction field of the power series $R[[x]]$?

I know that this field can be a proper subfield of $\operatorname{Frac}(R)((x))$, the Laurent series over the fraction field of $R$, as seen here. Given that, I'm at a loss of other candidates for what $\operatorname{Frac}(R[[x]])$ can be.

REPLY [3 votes]: I just want to share the following result of Philip Sheldon
(Trans. AMS Vol. 159, 1971):
Let $R\subset S$ be two subrings of the rational numbers.
Then the transcendence degree of the field extension
$\mathrm{Frac} (R[[x]])\subset\mathrm{Frac}(S[[x]])$
is infinite.