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normal closure (Definition)

Let $ K$ be an extension field of $ F$. A normal closure of $ K/F$ is a field $ L \supseteq K$ that is a normal extension of $ F$ and is minimal in that respect, i.e. no proper subfield of $ L$ containing $ K$ is normal over $ F$. If $ K$ is an algebraic extension of $ F$, then a normal closure for $ K/F$ exists and is unique up to isomorphism.



"normal closure" is owned by scanez.
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Cross-references: isomorphism, algebraic extension, subfield, minimal, normal extension, field, extension field
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This is version 2 of normal closure, born on 2002-11-16, modified 2002-11-16.
Object id is 3602, canonical name is NormalClosure.
Accessed 1958 times total.

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