Lemma 9.15.10. Let L/K be an algebraic normal extension of fields. Let E/K be an extension of fields. Then either there is no K-embedding from L to E or there is one \tau : L \to E and every other one is of the form \tau \circ \sigma where \sigma \in \text{Aut}(L/K).
Proof. Given \tau replace L by \tau (L) \subset E and apply Lemma 9.15.7. \square
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