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fixed field

(Definition)

Let be a field extension with Galois group $G = \operatorname{Gal}(K/F)$ , and let be a subgroup of . The fixed field of in is the set

$\displaystyle K^H := \{ x \in K \mid \sigma(x) = x$ for all $\displaystyle \sigma \in H \}.$

The set

is always a field, and $F \subset K^H \subset K$ .

"fixed field" is owned by djao. [ full author list (2) ]

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Cross-references: field, subgroup, Galois group, field extension
There are 23 references to this entry.

This is version 2 of fixed field, born on 2002-01-05, modified 2002-08-22.
Object id is 1325, canonical name is FixedField.
Accessed 3167 times total.

Classification:

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

Pending Errata and Addenda

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