I am trying to understand the proof for one direction of the following theorem:

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I am confused about the part in red. Why does this work? Has it something to do with the Frobenius endomorphism?

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    $\begingroup$ Exactly. That' because the Frobenius endomorphism is indeed an ring homomorphism. $\endgroup$ – Crostul Mar 18 at 20:20
  • $\begingroup$ @Crostul So the Frobenius function can be applied to polynomials? $\endgroup$ – numericalorange Mar 18 at 20:25
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    $\begingroup$ It can be applied in any commutative ring of characteristic $p$. In particular it can be applied to the ring of polynomials over a field with characteristic $p$. $\endgroup$ – Crostul Mar 18 at 20:31
  • $\begingroup$ Wow, thanks so much for clearing my head! $\endgroup$ – numericalorange Mar 18 at 20:31

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