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Galois extension

Galois extension noun: 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.

Noun

Galois extension (plural Galois extensions)

  1. (Galois theory) 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.

Examples of Galois extension in a sentence

  • 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.1986, D. J. H. Garling, A Course in Galois Theory, Cambridge University Press, page 108:
  • First, arithmetic obstructions against constructing central extensions of a fixed finite base Galois extension are analyzed with the local-global principle to give some quantitative estimates of them.1989, Katsuya Miyake, “On central extensions”, in Jean-Marie De Koninck, Claude Levesque, editors, Number Theory, Walter de Gruyter, page...

Forms of Galois extension

pluralGalois extensions

Origin of Galois extension

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

Words formed from Galois extension

  • differential Galois extension

Questions about Galois extension

What does Galois extension mean?
Galois extension means 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.
How do you use Galois extension in a sentence?
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.
What part of speech is Galois extension?
Galois extension is a noun.
What is the plural of Galois extension?
The plural of Galois extension is Galois extensions.

Words near Galois extension in the dictionary

  1. galoches
  2. galocitabine
  3. Galois
  4. Galois connection
  5. Galois connections
  6. Galois extension
  7. Galois extensions
  8. Galois field
  9. Galois fields
  10. Galois group
  11. Galois groups

Source and license

Adapted from Wiktionary: Galois extension (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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