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1、JohnR.DurbinModernAlgebraAnIntroductionSixthEditionJohnR.DurbinTheUniversityofTexasatAustinWILEYJohnWiley&Sons,Inc.PublisherLaurieRosatoneAssociateEditorShannonCorlissMarketingManagerJaclynElkinsMarketingAssistantTaraMartinhoProductionManagerDorothySinclairSeniorProductionEditorSandraDum
2、asDesignerJamesO'SheaSeniorMediaEditorMelissaEdwardsProductionManagementAptaracorplKellyRicciThisbookwassetin10/12TimesRomanbyAptaracorp,Inc.andprintedandboundbyHamiltonPrintingCompany.ThecoverwasprintedbyHamiltonPrintingCompany.Thisbookisprintedonacidfreepaper.19Copyright©2009,2005JohnW
3、iley&Sons,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections107or108ofthe1976UnitedStatesCopyrightAct,withouteithertheprior
4、writtenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.222RosewoodDrive,Danvers,MA01923,Websitehttp://www.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,11
5、1RiverStreet,Hoboken,NJ07030-5774,(201)748-6011,fax(201)748-6008,Websitehttp://www.wiley.com/go/permissions.Toorderbooksorforcustomerserviceplease,call1-800-CALLWILEY(225-5945).Durbin,JohnR.ModemAlgebra:AnIntroduction-6thed.ISBN-13978-0470-38443-5PrintedintheUnitedStatesofAmerica10987654
6、32ToJanePREFACEThisbookisanintroductiontomodem(abstract)algebraforundergraduates.Thefirstsixchapterspresentthecoreofthesubject,thebasicideasofgroups,rings,andfields.Theremainderisdesignedtobeasflexibleaspossible.Adiagramofchapterdependencies,precedingthetableofcontents,suggestsanumberofo
7、ptionsforintroducingvarietyanddepth.Afirstcourseinmodemalgebraoftenhastheadditionalgoalsofintroducingtheaxiomaticmethodandtheconstructionofproofs.Ihavetriedtokeepthesegoalsconstantlyinmind.Forexample,thefirstchaptertreatsideasthatareimportantbutneitherabstractnorcomplicat
