Revision #509 → #1096 · back to history
addedCommutative ring59bdd405b09e
addedRing of integersb49cdb8fa501
addedPolynomial ring1d91cf87cdbc
addedRing of continuous functions79df1e0c3bb4
addedZero divisor40b3ec39caed
addedIntegral domainb556971883e3
addedNilpotent element9005962dfd61
addedLocalization7ebd2a4d2c01
addedQuotient fieldfbc78cf2b64f
addedIdeals are two-sided680cecab4246
addedFree module7f794ac778e8
addedSubmodule of free module need not be freef275581d38c6
addedModule of finite typee24c936481aa
addedNoetherian characterization via finite type47506cd69daa
addedOnly ideals are zero and whole ring iff field83535e164b98
addedIdeal generated by a set7adbf48a9326
addedPrincipal ideal3e08dc808ce2
addedPrincipal ideal ring2704e924c858
addedPrincipal ideal domainb53cb5f58e34
addedPID is a UFDc40a539a0bb3
addedIrreducible element81881d505d3a
addedIrreducible polynomials73f402ad42ba
addedFundamental theorem of arithmetic6ee70c5b0160
addedPrime element36f9f1e48298
addedPrime implies irreducible in a domainb6059454ee84
addedFactor ring38675059b6b9
addedIntegers modulo ne03480787e1c
addedProper ideal67dc4959bc92
addedMaximal ideal977760dcb0de
addedMaximal ideal iff quotient is a field645dd40cc365
addedExistence of maximal idealsc66a469494a9
addedNoetherian ringabf6979c60cd
addedHilbert basis theorem69ca7f537d33
addedNoetherian approximationd15badd4e15a
addedArtinian ringab72aff44cd4
addedHopkins–Levitzki theoremf4e5ac9f8001
addedArtinian as zero-dimensional Noetherian503391adcab0
addedPrime ideale4d4a06884aa
addedFactorization into prime ideals in Dedekind ringseeddcbc7a169
addedMaximal ideals are prime1243ab1844b4
addedPrime ideal iff quotient is a domain2c6a52c929a5
addedLocal ring4593551270c0
addedSpectrum of a ring28dad4e2cc70
addedMaximal spectrum bijection (Nullstellensatz)556cd49991d4
addedMinimal primes and irreducible components71db88e57c83
addedFinitely many irreducible components for Noetherian Spec067c0284788f
addedPrimary decomposition517a4020a499
addedAffine scheme52d3d20e396a
addedRing recovered as global sectionsf61962c28e27
addedKrull dimensiona6086eeada76
addedDimension as supremum of prime chains95884b7d4dbe
addedA field is zero-dimensional495c5daf8492
addedNoetherian local rings have finite dimensionb0417f77d965
addedRing homomorphism23ad791a5fc2
addedKernel and image44b5110b0a2b
addedKernel is ideal, image is subring43edc629407e
addedRing isomorphismf9aebe7b108f
addedChinese remainder theorembca4e4a23cb8
addedZ is the initial commutative ringe60ea3698949
addedBinomial formula in commutative ringsf0e92c3c9bfc
addedTensor product of R-algebrasaffedc1e2cc7
addedFinitely generated algebraa89e804db9c7
addedFinitely generated moduleb1ba6545b7a8
addedLocal ring26bf3d505023
addedLocalization at a prime is local17094422d89a
addedResidue field57fadc92ce58
addedNakayama's lemma204330bf118a
addedCotangent space m/m^2748e3e30dd89
addedDimension inequality for Noetherian local ringsff1c3d5b9408
addedRegular local ring313b54e52b0e
addedRegularity iff associated graded is polynomial ring73d2fc6537e2
addedRegular local rings are UFDs95815ce8e251
addedDiscrete valuation ring6181029b61cd
addedDVRs are one-dimensional regular local rings7fef80b07582
addedGerms of holomorphic functions on a Riemann surfacedde7939b57cc
addedKrull's principal ideal theorem dimension bound6e51047a44c1
addedComplete intersection ringfd03d3d584cc
addedRegular local rings are complete intersections703a8ad78551
addedSet-theoretic complete intersection430496d67375
addedDepth of a local ring29d4862db6a7
addedDepth-dimension inequality300afbce22f2
addedCohen–Macaulay ring72ea49b2d24e
addedRegular local rings are Cohen–Macaulay5c4b1fc15cf3
addedNormal ring2a76a953b5de
addedNormal one-dimensional rings are regular0d202d8d63c3
addedI-adic topologybab09d6553d1
addedI-adic completionaaa57fc9670b
addedComplete ringdbc8a289d578
addedHensel's lemmade3674a9ecba
addedProjective module01c7ab81b2c0
addedFinitely generated projective over local ring is free49f9c2e02cf0
addedQuillen–Suslin theorem31f30f23d399
addedRegularity iff finite global dimension91bca1a3142f
addedExt functor265f605deab3
addedRegularity iff vanishing Ext619316dd6eac
addedBetti numbers and complete intersectionsd4a1e8708727
addedFlat module1a8383854e57
addedFinitely presented flat over local ring is freecfec3c26def1
addedFiber dimension of flat algebras3553104b87ac
addedWedderburn's little theoremc2cffa915432
addedJacobson's commutativity conditionb1d214eb3d0f
addedBoolean ringf737be7bd02c
addedGraded-commutative ring10dc496d27bc
addedCommutative differential graded algebra02a6b366b534
addedDifferential forms as a cdgac8e1b236dfd5
addedCohomology of a cdga is graded-commutativee5113e74b528
addedSuperalgebra74d5f72d83e9
addedAlmost commutative ring3dd294aff7a2
addedSimplicial commutative ring64a9e2e3d03f