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Definition 9.8.1. Consider a field extension $F/E$. An element $\alpha \in F$ is said to be algebraic over $E$ if $\alpha $ is the root of some nonzero polynomial with coefficients in $E$. If all elements of $F$ are algebraic then $F$ is said to be an algebraic extension of $E$.

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View Definition 9.8.1 as pdf