有限域思想的歷史演變.pdf

1、河北師范大學博士學位論文有限域思想的歷史演變姓名：鄧明立申請學位級別：博士專業(yè)：基礎數(shù)學指導教師：李文林康慶德20040520AbstractAsabranchofmodernalgebra，finitefieldsisallabstractsysteminalgebrawhichsatisfiesoperationallawssuchasassociativelawcommutativelaw，distributivelawetcTh

2、ispowerfulalgebraicstructurewithitsfinitenessmakesitselfaconciseandbeautifulsubjectofstudyinthemathematicalworldWithitseffectiveapplicationsinalotoftheoriesandpractice，finitefieldsbecomesgraduallyallimportant，well—recogn

3、ized，algebraictoolinmathematicsConsequentlyfinitefieldsattractsthestronginterestofmathematiciansTheformationanddevelopmentoffinitefieldstheoryhasalonghistoryOnthebasisofabundantmaterial，thepresentpapertriestosummarizeand

4、analyzethehistoryofideaoffinitefieldsinasystematicwayCenteringonthedevelopmentoffinitefields，thispaperilluminatesitsrelationshiptoabstractfieldsandexpoundstheideologicalconnectionsamongthemathematicianswhohadcontributedt

5、othetheory；atthesametime，thispaperpresentsitshistoricaldevelopmentfromtheprofessionalviewpointofthestructureoffinitefields；fmallythispaperintroducessomeapplicationsoffinitefieldstheoryDuetothelimitedspaceandtheauthor’sfi

6、eldofvision，thepresentpapercannotcovereveryaspectoffinitefieldstheoryandcanonlyemphasizesparticularlyonitsapplicationtocombinatoricsInconclusion，thispapermakesanattempttoexpoundtheprocessofevolutionofideaoffinitefieldsth

7、roughwhichwehaveacomprehensiveandclearerknowledgeoffinitefieldstheoryanditsrelationtoabstractfieldsFurthermore，wecangetageneralcommandofthedevelopmentofalgebraKeywords：Galoisfieldsfinitefieldsabstractfieldsalgebraicstruc