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**dori1123** Show that if the field $\displaystyle K$ is generated over $\displaystyle F$ by the elements $\displaystyle \alpha_1, \alpha_2, ..., \alpha_n,

$, where each $\displaystyle \alpha_i$ is not algebraic over $\displaystyle F$, then an automorphism $\displaystyle \sigma$ of $\displaystyle K$ fixing $\displaystyle F$ is uniquely determined by $\displaystyle \sigma(\alpha_1), \sigma(\alpha_2), ..., \sigma(\alpha_n)

$. In particular, show that an automorphism fixes $\displaystyle K $ if and only if it fixes a set of generators for $\displaystyle K$.

I think I need to define $\displaystyle K$, but I'm not sure how to do it. Can anyone help?