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1、AlgebraicNumberTheoryJ.S.MilneVersion3.02April30,2009AnalgebraicnumberfieldisafiniteextensionofQ;analgebraicnumberisanelementofanalgebraicnumberfield.Algebraicnumbertheorystudiesthearithmeticofalgebraicnumberfields—theringofintegersinthenumberfield,theidea
2、lsandunitsintheringofintegers,theextenttowhichuniquefactorizationholds,andsoon.AnabelianextensionofafieldisaGaloisextensionofthefieldwithabelianGaloisgroup.Classfieldtheorydescribestheabelianextensionsofanumberfieldintermsofthearithmeticofthefield.Thesenot
3、esareconcernedwithalgebraicnumbertheory,andthesequelwithclassfieldtheory.Theoriginalversionwasdistributedduringtheteachingofasecond-yeargraduatecourse.BibTeXinformation@misc{milneANT,author={Milne,JamesS.},title={AlgebraicNumberTheory(v3.02)},year={200
4、9},note={Availableatwww.jmilne.org/math/},pages={156+viii}}v2.01(August14,1996).Firstversionontheweb.v2.10(August31,1998).Fixedmanyminorerrors;addedexercisesandanindex;138pages.v3.00(February11,2008).Corrected;revisionsandadditions;163pages.v3.01(Sept
5、ember28,2008).Fixedproblemwithhyperlinks;163pages.v3.02(April30,2009).Fixedmanyminorerrors;changedchapterandpagestyles;164pages.Availableatwww.jmilne.org/math/Pleasesendcommentsandcorrectionstomeattheaddressonmywebpage.ThephotographisoftheForkHut,Huxl
6、eyValley,NewZealand.Copyrightc1996,1998,2008,2009,J.S.Milne.Singlepapercopiesfornoncommercialpersonalusemaybemadewithoutexplicitpermis-sionfromthecopyrightholder.ContentsNotations.......................................5Prerequisites...................
7、..................5Acknowledgements.................................5Introduction.....................................1Exercises......................................61PreliminariesfromCommutativeAlgebra7Basicdefinitions................................
8、...7Idealsinproductsofrings..............................8Noetherianrings...................................8Noetherianmodules.................................10Localrings.....................................10Ringsoffractions.................
