galois extension
Word Rarity
Very rare
Frequency: Zipf frequency 2.15 in modern English
23
Scrabble Score
15
Letters
4
Syllables
10
Unique Chars
Meaning
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.
Example Sentences
- "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."
- "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."
- "With the help of the results in Section 7.5 it is not hard to describe all Galois extensions. Proposition 7.6.1. Let E#47;F be a finite field extension. Then (i) E#47;F is a Galois extension if and only if it is normal and separable; (ii) E#47;F is contained in a Galois extension if and only if it is separable."
Etymology
Inflected Forms
Phrases
Frequently Paired Words
Galois group
Hopf-Galois extension