Revision #484 → #999 · back to history
addedAlgebraic number fielddd174fb02faf
addedFinite-dimensional vector spacee0448c85270e
addedNumber field (definition)c6b33c2089a3
addedRational numbers as smallest number field29667c749f74
addedGaussian rationals95e895de5d73
addedNonzero Gaussian rationals are invertiblec7d044f33b56
addedGaussian rationals are two-dimensional number field217a57afcea5
addedQuadratic field4c2ca387866c
addedCyclotomic field8f35ce21e840
addedReals and complexes are not number fields0d26823f4444
addedPairs of rationals is not a field4ea1fb311de3
addedAlgebraic field extension502b566a7a28
addedFinite-degree extensions are algebraic2382c1dcb4fe
addedMonic polynomial0582e575428c
addedAlgebraic integerdee24971e924
addedEvery integer is an algebraic integer8946e537768d
addedRational algebraic integer is an integer1e55cac2e53e
addedSum and product of algebraic integersa9e54ba482f5
addedRing of integersddb8e0296126
addedRing of integers is an integral domain20dce42753a2
addedNumber field is field of fractions of its ring of integers3d1589fcd017
addedDedekind ring5416a57e203e
addedUnique factorization of ideals12c707f8b5a8
addedFactorization of an ideal into prime idealse8d01ea257fc
addedFailure of unique factorization in quadratic integers507acece721e
addedEuclidean domains are unique factorization domainsdf0332be8fcc
addedIdeal class group is finite4157f74544fc
addedUnique factorization iff class number one843c3eef1e59
addedDedekind zeta function7aff81c506f2
addedClass number formula7e8e0e2b8a03
addedDirichlet's theorem on arithmetic progressionsb0d4e57292a2
addedIntegral basis4fc6b21e06c7
addedPower basis975a0a33cacd
addedPrimitive element theorem403d2bb5c454
addedPower integral basis and monogenic field7c7ad6700799
addedNon-monogenic field (Dedekind's example)b40a8c2f3b85
addedRegular representationdc5caed4cfa4
addedTrace and norm of a field elementa6e0830a69d4
addedTrace and norm computationa2c3bdaf5caf
addedLinearity of trace and multiplicativity of norm0aed33eb6429
addedTrace form0998c9befd94
addedDiscriminant of a number field21f0ef8d2472
addedAlgebraic integer iff characteristic polynomial is integral monicb7a35474ba59
addedIntegral basis and discriminant computationb494bad1877a
addedPlace of a number field255304f9e5dd
addedOstrowski's theorem for the rationals809dce0455c5
addedp-adic absolute value851e805d0d67
addedOstrowski's theorem (places of a number field)a49c01c230f0
addedSixth root of unity field embeddingse013239acf35
addedComputing Archimedean places (real and complex places)794d30f7b0ce
addedTotally real and totally complex fields8e2832a7ad18
addedUltrametric (non-Archimedean) placeb7a69447585f
addedUltrametric absolute value bounded by one on integers510a2758aeab
addedUltrametric place defines a prime idealc838cc2bf197
addedPrime ideal gives a discrete valuation123f28069efa
addedLocalization is a discrete valuation ring141f9e64db49
addedThree-way equivalence of places, prime ideals, localizationse862706e8ac0
addedGoing up and going down theorems5b38ab590455
addedIdeal lying over89bf4709d049
addedLying over theoremda04f0031374
addedRamification3c054a44d4bf
addedBranched covering of the power map1e4d7235d44f
addedRamification indices930552fd660c
addedRamified primebe91ac2d2445
addedRamification is a local property72067048cc77
addedRamification index computationadb40fa8d736
addedDedekind discriminant theorem3dba88dbe292
addedGalois group of cyclotomic field35608b5b7719
addedAbsolute Galois groupb14284f76d97
addedFundamental theorem of Galois theorye1b5fc18ac47
addedKronecker–Weber theorem95b44de62225
addedHilbert class field4b18d9e3e30f
addedBrauer group265e4b7e2619
addedGlobal fieldsf2c79469097b
addedHasse principlef9de0f989673
addedAdele ring and idelesb510b0f1d379