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Galois closure (Definition)

Let $ K$ be an extension field of $ F$. A Galois closure of $ K/F$ is a field $ L \supseteq K$ that is a Galois extension of $ F$ and is minimal in that respect, i.e. no proper subfield of $ L$ containing $ K$ is normal over $ F$.



"Galois closure" is owned by scanez.
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Cross-references: normal, subfield, minimal, Galois extension, field, extension field
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This is version 3 of Galois closure, born on 2002-11-16, modified 2006-10-15.
Object id is 3601, canonical name is GaloisClosure.
Accessed 2950 times total.

Classification:
AMS MSC: 12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)
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