Revision #264 → #1498 · back to history
addedProjective module (informal)0558a4b1385b
addedFree implies projective; converse failse5dff6c4029a
addedProjective is free over a PID (Quillen–Suslin)e9a628ec082d
addedLifting property characterizationd6d951a3a07c
addedSplit-exact sequence characterization0bf1799a90d5
addedDirect summand of free module characterizationa6f09a93745c
addedExact functor characterizationb786a677253b
addedDual basis characterizationfc940ddddd06
addedDirect sums/summands of projectives are projective883a88794bb5
addedRe is projective for idempotent e9bda4e85940c
addedIdeals of a product ring are projective not free342259f9e135
addedImplications among module propertiesabff70e6dc13
addedFree implies projective599e3d07ffc4
addedConverse over a field or skew field9841ea69382e
addedProjective abelian groups are free0c9a690b79e5
addedProjective is free over a local ring3b5f98506172
addedIdempotent ideals in a product ring are projective not freeb2709ae26723
addedNon-principal ideal over a Dedekind domain5fe884b2aed3
addedNatural module over a matrix ring47696470190d
addedModules over a semisimple ringb2a8c32f474c
addedProjective implies flat547bba947f31
addedQ is flat but not projectiveb29e812cd6e7
addedFinitely related flat implies projective032bbe6de95e
addedGovorov–Lazard: flat = direct limit of f.g. free1d8c8ad97b1b
addedRaynaud–Gruson characterization of projectivity6dd15a973828
addedProjectivity satisfies faithfully flat descente9479f8d9824
addedLeft hereditary ring72845f0e5381
addedQuotients of projectives need not be projective48dbb1c4f7e4
addedCategory of f.g. projectives is exact2982bb194130
addedProjective resolution8cd852e1ff3a
addedEvery module has a projective resolution2a2a7aa40d79
addedKoszul complex resolution3c82e485d6b3
addedLength of a finite resolution062fa3d49d0d
addedProjective dimension1ba1af214fb5
addedModules of projective dimension zero4904d6b9977b
addedLocalization of a projective module is projective6439217f7aa5
addedProjective over local ring is freea75d1e7e1ac7
addedLocally free = projective over Noetherian rings1b7b644873ac
addedLocally free non-projective over a Boolean ringd113d2b9681d
addedEquivalences for finitely presented modulese7d79a2b3d0f
addedConstant rank over a Noetherian integral domain86e5d75f9f75
addedA is a direct factor of B4d756102cc6b
addedRank at a prime idealfaf6bbf56b23
addedRank is locally constanta9f3d19fed94
addedConstant rank over connected spectrum64a0167c75d2
addedSerre–Swan theorem784b9b423e4a
addedVector bundles are locally freeaefec0176693
addedQuillen–Suslin theoreme9d892bfabe9
addedCounterexample for induction on variables9f8f72b7f835