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separable closure (Definition)

Let $ K$ be a field and let $ L$ be an algebraic closure of $ K$. The separable closure of $ K$ inside $ L$ is the compositum of all finite separable extensions of $ K$ contained in $ L$ (that is to say, the smallest subfield of $ L$ that contains every finite separable extension of $ K$).



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Cross-references: contains, subfield, contained, separable extensions, compositum, algebraic closure, field
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This is version 2 of separable closure, born on 2002-01-21, modified 2002-01-23.
Object id is 1514, canonical name is SeparableClosure.
Accessed 3183 times total.

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