Category:Field theory

A

• ► Algebraic number theory‎ (6 C, 125 P)

C

• ► Class field theory‎ (28 P)

F

• ► Field extensions‎ (10 P)

F cont.

• ► Finite fields‎ (61 P)
• ► Formally real field‎ (2 P)

G

• ► Galois theory‎ (33 P)

R

• ► Real closed field‎ (7 P)

• Field theory (mathematics)
• Glossary of field theory

A

• Abel's irreducibility theorem
• Abhyankar's inequality
• Additive polynomial
• Adjunction (field theory)
• Algebraic function field
• Algebraic number field
• Algebraically closed field
• All one polynomial
• Archimedean property

B

• Brauer–Wall group
• Brumer–Stark conjecture

C

• Characteristic (algebra)
• CM-field
• Complete field
• Composite field (mathematics)
• Conjugate element (field theory)
• Cubic field

D

• Differential Galois theory
• Discrete valuation

E

• Eisenstein's criterion
• Embedding problem
• Equally spaced polynomial
• Equivariant L-function
• Euclidean field
• Exponential field
• Exponentially closed field

F

• Field (mathematics)
• Field norm
• Field of fractions
• Field trace
• Finite field
• Formally real field
• Function field sieve
• Fundamental theorem of algebra

F cont.

• Fundamental theorem of Galois theory

G

• Galois group
• Galois theory
• Generic polynomial
• Global field
• Grothendieck's Galois theory
• Ground field

H

• Hardy field
• Hasse invariant of an algebra
• Higher local field
• Hurwitz problem
• Hyper-finite field
• Hyperreal number

I

• Isomorphism extension theorem
• Iwasawa theory

J

• Jacobson–Bourbaki theorem

K

• Krasner's lemma
• Kummer theory

L

• Levi-Civita field
• Linked field
• Liouville's theorem (differential algebra)
• List of number fields with class number one
• Local field

M

• Minimal polynomial (field theory)
• Multiplicative group

N

• Nagata's conjecture
• Norm form
• Normal basis

P

• P-adic number
• P-adically closed field
• Perfect field
• Polynomial basis
• Primary extension
• Primitive element (finite field)
• Primitive element theorem
• Primitive polynomial (field theory)

P cont.

• Pseudo algebraically closed field
• Pseudo-finite field
• Purely inseparable extension
• Pythagoras number
• Pythagorean field

Q

• Quadratic field
• Quadratically closed field
• Quasi-algebraically closed field
• Quasi-finite field
• Quaternionic structure

R

• Ramification theory of valuations
• Rational number
• Rational variety
• Real closed field
• Regular extension
• Resolvent (Galois theory)
• Rupture field

S

• Separable polynomial
• Serre's conjecture II (algebra)
• Splitting field
• Square class
• Stark conjectures
• Strassmann's theorem
• Stufe (algebra)
• Superreal number

T

• Tensor product of fields
• Thin set (Serre)
• Totally real number field
• Transcendence degree
• Tschirnhaus transformation
• Tsen rank

U

• U-invariant
• Universal quadratic form

V

• Valuation (algebra)
• Valuation ring