Galois theory

E157385

branch of abstract algebra branch of mathematics

Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (4)

Label	Occurrences
Galois theory canonical	12
Galois Theory	1
Galois’ theory of equations	1
fundamental theorem of Galois theory	1

Statements (49)

Predicate	Object
instanceOf	branch of abstract algebra ⓘ branch of mathematics ⓘ
addresses	solvability of polynomial equations by radicals ⓘ
appliesTo	algebraic extensions ⓘ algebraic number fields ⓘ finite fields ⓘ function fields ⓘ
centralConcept	Galois correspondence ⓘ Galois group ⓘ automorphism ⓘ discriminant ⓘ field extension ⓘ fixed field ⓘ intermediate field ⓘ normal extension ⓘ resolvent ⓘ separable extension ⓘ splitting field ⓘ
characterizedBy	Galois correspondence between subgroups and intermediate fields ⓘ correspondence between normal subgroups and subextensions ⓘ
field	abstract algebra ⓘ
hasApplication	classification of finite extensions of the rationals ⓘ construction of ruler-and-compass constructible numbers ⓘ
hasSubfield	algebraic number theory applications ⓘ classical Galois theory ⓘ differential Galois theory ⓘ infinite Galois theory ⓘ inverse Galois theory ⓘ
historicalOrigin	19th century ⓘ
implies	general quintic is not solvable by radicals ⓘ
namedAfter	Évariste Galois ⓘ
relatedTo	field automorphisms ⓘ group actions ⓘ solvable groups ⓘ
relates	field extensions to groups of automorphisms ⓘ
studies	field extensions ⓘ polynomial equations ⓘ symmetry of roots of polynomials ⓘ
toolFor	algebraic geometry ⓘ algebraic number theory ⓘ coding theory ⓘ cryptography ⓘ
usesConcept	field theory ⓘ Galois theory self-linksurface differs ⓘ surface form: fundamental theorem of Galois theory group theory ⓘ normal closure ⓘ primitive element theorem ⓘ ring theory ⓘ separability ⓘ

Referenced by (15)

Full triples — surface form annotated when it differs from this entity's canonical label.

construction of the regular 17-gon with straightedge and compass → isLinkedTo → Galois theory ⓘ

Évariste Galois → fieldOfWork → Galois theory ⓘ

Évariste Galois → notableWork → Galois theory ⓘ

Abel–Ruffini theorem → field → Galois theory ⓘ

Abel–Ruffini theorem → relatedTo → Galois theory ⓘ

this entity surface form: Galois’ theory of equations

Emil Artin → fieldOfWork → Galois theory ⓘ

Ian Stewart → notableWork → Galois theory ⓘ

this entity surface form: Galois Theory

Gaussian periods → relatedTo → Galois theory ⓘ

Galois theory → usesConcept → Galois theory self-linksurface differs ⓘ

this entity surface form: fundamental theorem of Galois theory

quadratic reciprocity law → proofMethodsInclude → Galois theory ⓘ

quadratic reciprocity law → influencedDevelopmentOf → Galois theory ⓘ

Noether field → studiedIn → Galois theory ⓘ

Galois → knownFor → Galois theory ⓘ

subject surface form: Évariste Galois

Galois → hasNotableAssociation → Galois theory ⓘ

Galois group → field → Galois theory ⓘ