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1、SpringerMonographsinMathematicsAntonioJ.EnglerAlexanderPrestelValuedFieldsABCAntonioJ.EnglerAlexanderPrestelDepartamentodeMatemáticaFak.MathematikIMECC-UNICAMPFachbereichMathematikundStatistikCx.Postal6065Postfach556013083-970Campinas78457KonstanzBrazilGermanyE-mail:engler@ime.unicamp.brE-mail:alex.
2、prestel@uni-konstanz.deLibraryofCongressControlNumber:2005930440MathematicsSubjectClassification(2000):12J10,12J20ISSN1439-7382ISBN-103-540-24221-XSpringerBerlinHeidelbergNewYorkISBN-13978-3-540-24221-5SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorp
3、artofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initsc
4、urrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringeronline.comcSpringer-VerlagBerlinHeidelberg2005PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,tr
5、ademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-f
6、reepaperSPIN:1099684341/TechBooks543210TothememoryofOttoEndler(17.9.1929–12.5.1988)PrefaceThepurposeofthisbookistogiveaself-containedandcomprehensiveintro-ductiontothetheoryofgeneralvaluations,incontrasttoclassicalabsolutevalues.Inparticular,wepresentsomeapplicationsofthegeneraltheorygoingbeyondtheu
7、seofabsolutevalues.Thebookdoesnotaimforanencyclopaedicpresentation,butratherprefersastreamlinedstyle,leadingeventuallytodeepresultsofrecentresearch.Whiletheclassicaltheoryofabsolutevaluescanbefoundinm