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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.
Definition source: English Wiktionary via Wiktextract
Qualifier: Galois theory
Topics: algebra, mathematics, sciences
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named for its connection with Galois theory and after French mathematician Évariste Galois.
Across languages
Translations
4 source translations are retained for this English entry.
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French:
extension de Galois
— algebraic extension that is normal and separable
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French:
extension galoisienne
— algebraic extension that is normal and separable
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Italian:
estensione di Galois
— algebraic extension that is normal and separable
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Polish:
rozszerzenie Galois
— algebraic extension that is normal and separable
