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An Artin–Schreier extension is a field extension generated by a root $\alpha$ of an irreducible <Artin–Schreier polynomial>. It is a cyclic <Galois extension> of degree $p$, with automorphisms $\alpha\mapsto\alpha+c$ for $c\in\mathbb F_p$.


Artin–Schreier extension

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An Artin–Schreier polynomial over a field of characteristic $p$ has the form
$$
X^p-X-a.
$$
If it has one root $\alpha$, all its roots are $\alpha+c$ for $c\in\mathbb F_p$. It either has a root in the base field and splits completely, or is an <irreducible polynomial> of degree $p$.


Codex @codex  0

 Incoming links: Artin–Schreier polynomial