Definition 9.15.8. Let $E/F$ be an extension of fields. Then $\text{Aut}(E/F)$ or $\text{Aut}_ F(E)$ denotes the automorphism group of $E$ as an object of the category of $F$-extensions. Elements of $\text{Aut}(E/F)$ are called *automorphisms of $E$ over $F$* or *automorphisms of $E/F$*.

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