Definition 10.45.5. Let $k$ be a field. The field extension $k'/k$ of Lemma 10.45.4 is called the perfect closure of $k$. Notation $k^{perf}/k$.

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).