Revision #651 → #1544 · back to history
addedRing (informal)af98e520dcc1
addedRing (formal)f77e99019397
addedCommutative ringe542ad06eec4
addedRing axioms2d9285f4c13f
addedDivision ring and field961c4359bd8e
addedAdditive group of a ring is abelian808d528f5f71
addedIntegers as a ring63b20e979c29
addedBasic properties of a ring266aad3b589c
addedIntegers modulo 481fba606365f
addedRing of 2-by-2 matrices over a field14d55f30a79c
addedMatrix ring over a ringbb3ffc7ca4c7
addedRing of integers (prototypical commutative ring)d5d130430b1f
addedRational, real, complex numbers as fieldseb08cf2e8099
addedUnital associative algebra over commutative ring487f0b30cfc2
addedPolynomial algebra R[X]695b95bcd7e4
addedContinuous real-valued functionse634d2e17a7b
addedFunctions from a set to a ring790da2ffc093
addedRing of quadratic integers97ced4ba60ae
addedRing of profinite integers1aae571f75e5
addedHecke ring0e6dd7fb0380
addedBoolean ring on a power set1dde0b85f909
addedMatrix ring (noncommutative)1d1cb7cead13
addedEndomorphism ring of an abelian group0f053c6ec4bb
addedEndomorphism ring of an elliptic curveda26c39173ec
addedGroup ring27c7157e18c2
addedRing of differential operatorsf2ffc81f6c30
addedNatural numbers are not a ringa3b1c78d7197
addedConvolution rng (Dirac delta)ccf7f83aa45c
addedProduct of a sequence in a ring8f22da405f91
addedNonnegative integer powersb7ef97e20fbc
addedLeft zero divisor4dfde1d63dd1
addedNilpotent element21f77ad66a95
addedNilpotent is a zero divisor8667dc87d941
addedIdempotent element96bbe6f9593c
addedUnit in a ring3ab786e433c1
addedIntersection of subrings is a subringe5f15a4f2b17
addedSubring generated by a set3263be6b8cd9
addedCharacteristic subring and characteristicfc598a5716d4
addedCenter and centralizer of a ring14242ed58146
addedLeft ideal2b581684af14
addedRight ideal and two-sided ideal26bdbb2d2404
addedPrincipal idealcb9a8487d08a
addedSimple ringe5de2ee696df
addedCommutative simple rings are fields62dffa8b5517
addedNoetherian and Artinian ringsb4dbd15f2a88
addedHopkins–Levitzki theorem593651285131
addedPrime idealddb65876294b
addedRing homomorphismb15c04b37521
addedRing isomorphismbbda90bf9ea7
addedReduction modulo 4 homomorphism0806ac881bcd
addedInner automorphism176d1d1fa5e9
addedFrobenius homomorphismf65610239d78
addedGalois groupbbfaa2620a5d
addedRepresentation of an algebrae6c22a8fa817
addedKernel of a ring homomorphism0e68b415926a
addedHomomorphism to center = algebra structure636aa2f31b69
addedQuotient ring9c610af678f8
addedUniversal property of quotient ring075c0b887bb1
addedFirst isomorphism theorem for ringsb8a65199e8b4
addedModule over a ring5c9bc2636589
addedRing homomorphism induces module structure98221087e630
addedDirect product of rings8394b052c2b9
addedChinese remainder theoremd0d09d92649e
addedFinite direct product as direct sum of ideals0c45f7b7b9af
addedPolynomial ring7b677be8e770
addedProperties of polynomial ringsf63396ca87e3
addedSubstitution homomorphismcfe0b180c488
addedSubalgebra generated by t^2 and t^3ba2a059d0e51
addedDerivative from polynomial substitution60f835ec52d0
addedUniversal property of polynomial ring7021a52e4fd0
addedMonic polynomial factors over an extensione1d226ddd1ff
addedHilbert's Nullstellensatz8d97600d8ce3
addedFormal power series ring32cb63e26981
addedMatrix ring M_n(R)65a7b27c4ec3
addedEndomorphism ring End_R(U)f803610fc5ec
addedMatrix ring as endomorphism ringb2e42efcc279
addedSchur's lemmad0e42b4f5190
addedArtin–Wedderburn theoremac048f37fbd2
addedMorita equivalence of R and M_n(R)c23fd78faaff
addedFiltered colimit (union) of rings824c4deac3b2
addedEvery ring is a filtered colimit of finitely generated subringsf25ceb5be9b8
addedProjective limit of rings78243f1f2c46
addedLocalization of a ring2a1f079ac824
addedLocalization of a modulee103b615adf6
addedPrime ideals under localization08a443596160
addedLocalization is exactcdd6c83fceaa
addedExactness from local exactnessd3320e6bd8c6
addedCompletion of a ring at an ideal472468cd7a1f
addedKrull's intersection theoremdfceb423861f
addedRing of p-adic integers281e807fe417
addedp-adic absolute valued96e6059f1c3
addedCohen structure theoremec17d2e9b2db
addedFree ring8625460deaa7
addedUniversal property of free ring2663ae42bbe8
addedRing with generators and relationsf43d224380a8
addedTensor product of algebrasb4a73ec2c36d
addedDomain and integral domainebb06c37ba5b
addedPrincipal ideal domain80225fd63de6
addedUnique factorization domain25e1f9efb89b
addedStructure theorem for finitely generated modules over a PID436683e3f30b
addedRegular local rings are UFDsa8ca7da236ea
addedDivision ringbaedb6b1f309
addedCentralizer in a division ring14f739e64d67
addedWedderburn's little theoremfdb20438ef8e
addedModules over a division ring are free5528831ac7d6
addedCyclic algebrad99b827fde54
addedSemisimple module and ring2ef63300abaa
addedDivision ring is semisimplef90ba587ae19
addedMatrix ring over a division ring is semisimplebc54799a3b73
addedMaschke's theoreme3b6c55b6d76
addedClifford algebras are semisimplec76bb5796fa0
addedWeyl algebra is simple but not semisimplecff7e0dede70
addedModules over a semisimple ring are semisimple81b3d6c0ce15
addedCharacterizations of semisimple ringsd637b3981b93
addedSeparable algebra91a5a42acc95
addedCentral simple algebraeb4fbcd17df0
addedSkolem–Noether theorem7733b98e7712
addedSimilarity of central simple algebrasdb512bf6750e
addedBrauer groupdb8009327743
addedBrauer groups of standard fieldsd2ec5e78afa0
addedBr(F/k) for finite Galois extensions39cfe2fc82b4
addedAzumaya algebrad7205446b304
addedValuationd8ae2c9b3617
addedValuation ringbdc6fbd47f79
addedValuation on formal Laurent series910b2a6d17f0
addedGroup ring with totally ordered group4f2e20c9e8a5
addedAssociative algebra42e47ddcbd46
addedTopological ring0dd76ed08124
addedLambda-ring2bf9a7b0038c
addedTotally ordered ring934ccdc3d377
addedIntegral cohomology ringa651461a1315
addedBurnside ring of a groupd0573a28ce1a
addedRepresentation ringfdf69307e4be
addedFunction field of an algebraic varietyc065ee042e51
addedFace ring (Stanley–Reisner ring)c62df394173f
addedRing as monoid in Ab0d434173972a
addedRing as endomorphism ring of an abelian X-groupe425830ab077
addedRing as preadditive category with one objectc406ddd05bbf
addedRng (generalization)5c4da7fa925d
addedNonassociative ring9bd2012e5ee4
addedSemiringed774b1f19b6
addedNon-negative integers as a semiringe99e4e62483d
addedRing object in a categorycc5035296e75
addedRing schemecb834c9a5314
addedWitt vector ring scheme W_n4fed02f3f40d
addedRing spectrumb4700dcc7664