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Galois conjugate (Definition)

Let $ K$ be a field, and let $ L$ be a separable closure. For any $ x \in K$, the Galois conjugates of $ x$ are the elements of $ L$ which are in the orbit of $ x$ under the group action of the absolute Galois group $ G_K$ on $ L$.



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Cross-references: absolute Galois group, group action, orbit, separable closure, field

This is version 3 of Galois conjugate, born on 2002-01-21, modified 2002-08-22.
Object id is 1519, canonical name is GaloisConjugate.
Accessed 2035 times total.

Classification:
AMS MSC: 12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)
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Galois conjugates? by archibal on 2004-04-06 00:26:03
If L is not a Galois extension of K, are the Galois conjugates of x really only the images of x that lie in L? I thought they would include the entire orbit of x under the Galois group.
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