Category:Field theory

• Field (mathematics)
• Glossary of field theory

A

• Abel's irreducibility theorem
• Abhyankar's inequality
• Algebraic element
• Algebraic function field
• Algebraic independence
• Algebraic number field
• Algebraically closed field
• All one polynomial
• Archimedean property

B

• Brauer–Wall group

C

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

D

• Discrete valuation

E

• Eisenstein's criterion
• Equally spaced polynomial
• Euclidean ordered field
• Exponential field

F

• Field of fractions
• Field trace
• Formally real field
• Function field of an algebraic variety
• Function field sieve
• Fundamental theorem of algebra

G

• Generic polynomial
• Global field
• Golden field
• Ground field

H

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

I

• Infrastructure (number theory)
• Isomorphism extension theorem
• Iwasawa theory

J

• Jacobson–Bourbaki theorem
• Joubert's theorem

K

• Krasner's lemma
• Kummer theory

L

• Linked field
• Liouville's theorem (differential algebra)
• List of number fields with class number one
• Local field
• Locally compact field
• Lüroth's theorem

M

• Minimal polynomial (field theory)
• Multiplicative group

N

• Nagata's conjecture
• Norm form
• Normal basis

O

• Ordered exponential field

P

• P-adic number
• P-adically closed field
• P-basis
• Perfect field
• Primitive element theorem
• Primitive polynomial (field theory)
• 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
• Quasifield
• Quaternionic structure

R

• Ramification theory of valuations
• Rational number
• Rupture field

S

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

T

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

U

• U-invariant
• Universal quadratic form

V

• Valuation (algebra)
• Valuation ring