Galois Extension Definition

noun

(algebra GALOIS EXTENSION that is both a normal and a separable extension ; equivalently, an algebraic extension E/F such that the fixed field of its automorphism group (Galois group ) Aut(E/F) is the base field F.

The significance of a Galois extension is that it has a Galois group and obeys the fundamental theorem of Galois theory .

The fundamental theorem of Galois theory states that there is a one-to-one correspondence between the subfields of a Galois extension and the subgroups of its Galois group.

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