Field extension

A field extension is a homomorphism of fields $K\hookrightarrow L$ . It is denoted as $K\subseteq L$ .

Any homomorphism of fields is injective, so $K$ can be identified with its image in $L$ ; we simply regard $K$ as a subfield of $L$ .

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Let $E$ be a field extension of $\R$ of odd degree. Show that $E=\R$ .

Open exercise

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