# Example of infinite perfect field with char $p$

All finite fields (they have char $$p$$ for some $$p$$ prime) are perfect. A well known field which is not finite and not perfect with char $$p$$ is $$\mathbb{F}_p(t)$$, the field of rational functions with values in $$\mathbb{F}_p$$ with an unknown $$t$$.

Can someone show me an example of perfect, infinite field with char $$p$$?

A trivial example is the algebraic closure of $$\Bbb F_p(t)$$.
• @Gabrielek how about algebraic closure of $\mathbb{F}_p$? It is perfect and you can describe all its elements. – Slup Dec 30 '19 at 14:30
• @Paul K $\mathbb{C}$ is algebraically closed over $\mathbb{R}$ but it has char $0$ – Gabrielek Dec 30 '19 at 14:30
• $\bigcup_n \Bbb{F}_p(t^{1/p^n})$ is easier to visualize – reuns Dec 30 '19 at 14:33