[Dr._Daniel_A._Marcus__(auth.)]_Number_Fields....

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1、DanielA.MarcusNumberFieldsSpringerDr.DanielA.MarcusDepartmentofMathematicsCalifomiaStatePolytechnicUniversityPomona,CA91768USAEditorialBoard(NorthAmerica)S.AxlerF.w.GehringDepartmentofMathematicsDepartmentofMathematicsMichiganStateUniversityUniversit

2、yofMichiganEastLansing,MI48824AnnArbor,MI48109USAUSAP.R.HalmosDepartmentofMathematicsSantaClaraUniversitySantaClara,CA95053USAMathematicsSubjectClassification(1991):12-01,12Axx,12Cxx,11Rxx,11TxxLibraryofCongressCataloginginPublicationDataMarcus,Danie

3、lA.1945-Numberfields.(Universitext)"Thisbookgrewoutofthelectureofacourse.atYaleUniversityinthefalisemester,1972."Bibliography:p.Includesindexes.1.Algebraicnumbertheory.2.Fields,Algebraic.I.Title.QA247.M346512'.7477·21467Allrightsreserved.Nopartofthis

4、bookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag,Printedonacid-freepaper.©1977bySpringer-Verlag,NewYorkInc,987654ISBN978-0-387-90279-1ISBN978-1-4684-9356-6(eBook)00110.1007/978-1-4684-9356-6Tomyparents,SelmaandLouis

5、MarcusAcknowledgmentsIthankJohnYangforthedeterminationofthealgebraicintegersinabiquadraticfield(exercise42,chapter2)andDodieShapirofortheverycarefulfinaltyping,whichiswhatyouseehere.Also,thanksgotomywifeShelleyforherunfailingwitandtomysonAndrew,age4,

6、forhischeerfulpresence.TableofcontentsFOREWORD.viiCHAPTER1:ASPECIALCASEOFFERMAT'SCONJECTURE1CHAPTER2:NUMBERFIELDSANDNUMBERRINGS12CHAPTER3:PRIMEDECOMPOSITIONINNUMBERRINGS55CHAPTER4:GALOISTHEORYAPPLIEDTOPRIMEDECOMPOSITION98CHAPTER5:THEmEALCLASSGROUPAND

7、THEUNITGROUP•130CHAPTER6:THEDISTRIBUTIONOFIDEALSINANUMBERRINGCHAPTER7:THEDEDEKINDZETAFUNCTIONANDTHECLASSNUMBERFORMULA182CHAPTER8:THEDISTRIBUTIONOFPRIMESANDANINTRODUCTIONTOCLASSFIELDTHEORY••••••••223APPENDIX1:CCMMUTATIVERINGSANDIDEALS251APPENDIX2:GALO

8、ISTHEORYFORSUBFIELDSOFCAPPENDIX3:FINITEFIELDSANDRINGS265APPENDIX4:'LWOPAGESOFPRIMESFURTHERREADINGINDEX•••••273INDEXOFTHEOREMSLISTOFSYMBOLSForewordThisbookgrewoutofthelecturenotesofacoursewhichIgaveatYaleUniversityintheFallsemester,1972.Exerciseswerea