If $K$ is a separable algebraic extension of a field $F$, then its **Galois closure** is the smallest extension field, in terms of inclusion, which contains $K$ and is Galois over $F$. If $K=F(\alpha)$ where $\alpha$ has irreducible polynomial $f$ over $F$, then the Galois closure of $K$ is the splitting field of $f$ over $F$.

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- Last edited by Alina Bucur on 2018-07-07 22:10:54

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- 2018-07-07 22:10:54 by Alina Bucur (Reviewed)