Field theory MOC

Frobenius endomorphism

Let 𝐾 be a field of prime characteristic 𝑝. The Frobenius endomorphism 𝜎 :𝐾 →𝐾 is defined by field

𝜎(𝑥)=𝑥𝑝

which is indeed an endomorphism by the Freshman’s dream. This is surjective, and thus a Frobenius automorphism, precisely when 𝐾 is a Perfect field.

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