拓?fù)浞执蜟--代數(shù)的不變理想.pdf

1、上海師范大學(xué)碩士學(xué)位論文拓?fù)浞执蜟代數(shù)的不變理想姓名：徐靜申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：許慶祥20070401AbstractThispaperconsistsofthreeparts：IntroductionsofHilbertC‘modules，TopologieaUy口adedToeplitzcrosssectionalalgebrasoverFellbundles，ThePrimitiveidealsandInvar

2、iantidealsofToeplitzalgebrasInthefirstcharpter，weintroducethefundamentalofHilbertC一modulesandtheconceptsandbasictermswhichisreadyforthispaperInthesecondcharpter，wefirstlyintroduceandstudytheToeplitzcrosssectionalalgebrao

3、ndiscretegroups，whichisthenatllralgeneralizationofgroupC一algebrasandFellbundlesGivenaFellbundle召=(Bt)壇roveradiscretegrouprForanynonemptysubsetEofr，aToeplitzcrOSSsectionalalgebraTEisintroduced，andweprovethattheToeplitzcro

4、sssectionalalgebraTeistopologicallygradediftheFellbundle8=(Bt)t∈PisregularwithrespecttothegivensubsetEInthethirdcharper，westudytwokindsofidealsofToeplltzalgebras：primitiveidealsandinvariantidealsLet(G，G)beadiscreteabelia

5、norderedgroup，denoteby丁GtheassociatedToeplitzalgebraTheprimitiveidealsof丁GwerefirstlystudiedbyAdjiandRaebumin[1s]Inthispaper，we’Ugiveamuchsimplerproofoftheirresult(【13】，Corollary34)AnotherimportantRspectofthestudyaboutTo

6、eplitzalgebrasistheiridealstnlctur島Inthispaperwefirstlyintroducetheconceptof豇invariantidealanddiscns8therelationshipamongdiagonalinvariantideals，invariantidealsand垂invariantidealsofToeplltzalgebrasSpeciallywegiveanexampl

7、eofaninvariantidealofcertainToeplltzalgebra，whichisnotdiagonalinvariantKeywords：Fellbundle；Toeplitzcroftssectionalalgebra；Conditionalexpectation；Abelianorderedgroup；Toeplitzalgebra；Primitiveideal；Diagonalinvariantideal；I