fundamental theorem of Galois theory
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
finite Galois extensions
|
| gptkbp:category |
theorem in mathematics
theorem in algebra |
| gptkbp:correspondenceType |
inclusion-reversing
|
| gptkbp:describes |
correspondence between subfields and subgroups
|
| gptkbp:field |
gptkb:Galois_theory
abstract algebra |
| gptkbp:formedBy |
gptkb:Évariste_Galois
|
| https://www.w3.org/2000/01/rdf-schema#label |
fundamental theorem of Galois theory
|
| gptkbp:implies |
Galois group of an extension is isomorphic to quotient group
fixed field of a subgroup is an intermediate field normal subgroups correspond to normal extensions |
| gptkbp:namedAfter |
gptkb:Évariste_Galois
|
| gptkbp:publishedIn |
gptkb:Galois'_memoir_(1846,_posthumously)
|
| gptkbp:relatedTo |
gptkb:fundamental_theorem_of_algebra
finite field automorphism group normal extension separable extension solvable group |
| gptkbp:state |
there is a one-to-one correspondence between intermediate fields and subgroups of the Galois group
|
| gptkbp:usedIn |
solvability of polynomials
classification of field extensions |
| gptkbp:bfsParent |
gptkb:Weyl_group
gptkb:Galois_theory |
| gptkbp:bfsLayer |
5
|