Lemma 15.115.8. Let $A$ be a discrete valuation ring. Assume the reside field $\kappa _ A$ has characteristic $p > 0$ and that $a \in A$ is an element whose residue class in $\kappa _ A$ is not a $p$th power. Then $a$ is not a $p$th power in $K$ and the integral closure of $A$ in $K[a^{1/p}]$ is the ring $A[a^{1/p}]$ which is a discrete valuation ring weakly unramified over $A$.
Proof. This lemma proves itself. $\square$
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)
There are also: