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Galois extension

noun

Etymology

Named for its connection with Galois theory and after French mathematician Évariste Galois.

  1. derived from mathematician Évariste Galois

Definitions

  1. An algebraic extension that is both a normal and a separable extension

    An algebraic 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.
    • Corollary If L#58;K is a Galois extension, there exists an irreducible polynomial f in K#91;x#93; such that L#58;K is a splitting field extension for f over K.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA