Revision #464 → #1220 · back to history
addedField (informal lead)5abd926df97f
addedField (informal)6fa4572df04c
addedField (classic axiomatic)11f642a0b855
addedField as commutative ringb27adfc978e6
addedField (alternative axiomatizations)e175cf0a70ea
addedField of rational numbersd4cf8d136ce1
addedField of real numbersfc43a417944d
addedField of complex numbers69c15670794d
addedField of constructible numbers5004e0b35c8c
addedField with four elements F42a84461f37e4
addedEvery field is an integral domainaac8a4ea119d
addedAdditive group of a fieldc17d65253804
addedNonzero elements form a multiplicative group21a2a9258ae8
addedFinite subgroups of multiplicative group are cyclic57578a56c143
addedCharacteristic of a field173f48ec318c
addedCharacteristic is prime2f0358aa0f03
addedFrobenius is a field homomorphism2a659b6df073
addedSubfield270d1dcdc60f
addedField homomorphism0930bf6d0a74
addedField homomorphisms are injectiveed635856cc43
addedPrime fieldc28a5995c33d
addedEvery field contains a prime field8da31978f8e5
addedFinite fieldc354883ffd5a
addedOrder of finite field is prime power9d4c6fd6c294
addedConstruction of finite field via splitting field2468073b3fda
addedFinite fields of same order are isomorphic8b3f873b001d
addedCommutative ringcedc7dfcb03e
addedCharacterization of fields among commutative rings49573c581437
addedField of fractions99d0ca199ca9
addedFractions of an integral domain form a fieldda260817b7af
addedResidue fieldccef935f064e
addedMaximality of (f) iff f irreducible1c821e832800
addedSubfield generated by an element08813eed5a43
addedCompositum of subfieldse34b818151de
addedField extensiond42c9584fd4b
addedDegree of a field extension701720d8c162
addedMultiplicativity of degrees (tower law)ea3f95e50ecb
addedAlgebraic element1f8c202f7260
addedAlgebraic extension0888e4efd057
addedFinite extensions are algebraic7d771ecf0a99
addedE(x)/E algebraic iff x algebraic1125d843629d
addedTranscendental element4a33a3acd7b8
addedTranscendence basisb7e21ee16047
addedExistence of transcendence basisac70eda664f1
addedAlgebraically closed field3bfb67892e1c
addedFundamental theorem of algebra99c24b3f7b83
addedAlgebraic closure4e7e9b057920
addedArtin–Schreier theorem (real closed fields)7a46961b860c
addedExistence and uniqueness of algebraic closurea61fb9cd9700
addedOrdered field186a6566d86e
addedArtin–Schreier (orderable iff formally real)118dd6d7846a
addedArchimedean field3d6534534dd9
addedDedekind-complete ordered fieldf90e7761fec9
addedComplete implies Archimedeanbe41f67b0b39
addedUniqueness of complete ordered field Rdd08577029d5
addedTopological field07345597fb03
addedLocal field88809aa9beeb
addedAx–Kochen theorem3db788950797
addedDifferential field30e9830b8abf
addedFinite Galois extension51bbc022e602
addedPrimitive element theorem1640846c6f97
addedGalois group393122c75c3e
addedFundamental theorem of Galois theory477bc532410a
addedAbel–Ruffini theorem4722f4eb193b
addedGalois extension via tensor product8b291f0d17b3
addedClassification of algebraically closed fields5018c563f5fd
addedElementarily equivalent fields6ef2099d7d00
addedLefschetz principle4a8532794688
addedŁoś's theorem45d18f19acbb
addedAbsolute Galois group083972d870c6
addedAbsolute Galois group of finite field7a3f5896fb2f
addedMilnor K-theory1bbe1bff287a
addedNorm residue isomorphism theoremcea97fe08012
addedMatsumoto's theoremcb5a68b6555c
addedUnique solution of ax = b in a field17443ecb8754
addedField of functions8a2499393a61
addedFunction field of an algebraic variety6fe052711713
addedGlobal fieldf88bed853420
addedCyclotomic field9f9a99623353
addedOstrowski's theoreme5a24c7e830f
addedHasse–Minkowski theoremab23d23abf3d
addedKronecker–Weber theorem857e4bd4c4a7
addedField with one element2792e2b39490
addedDivision ring (skew field)ce5b31357597
addedFrobenius theorem on division algebras844e8a297372
addedWedderburn's little theorem8b10258b0163