分次Bass環(huán)及其對偶.pdf

1、福建師范大學(xué)碩士學(xué)位論文分次Bass環(huán)及其對偶姓名：李長安申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：陳清華2001.4.5GradedBassringanddualityAbstract：TileGradedringtheoryoccupiesthecentxalpartonthestudyofringtheoryInrecelltyearsmanyalgebralistssuchasJEBjSrhFVanOystaeyenCN&stg

2、sescuSMontgonleryDPassnlanMBeattieLiuShaoxuebasedtilestudyofgradedringstructureOilC’一AlgebrawhichnlakesgreatfurtherachivelnelltillthisbrmlchOilintroducinggradedHanlshermodule(iegradedBassmodule)&lidgradedSenfiartinianmod

3、uletilethesisdiscussestilechar—acterizationoftileaccordingmoduleclassWithtilehelpofgradedJocobsonradical(Socle)gradedmaxinlal(minimal)subnlodulegradedcogeneratorandgradedinjectivehullgradedBassfSen正artiIllringisthoroughl

4、ycharacterizedAgainusingSmashproductsExcellentEx—tensionsecttileauthordiscussestilerelationsanlonggradedringRandtilerings(冗R，R車G)whicharederivedbyitAndobtainsRRfR#GandgradedringRareidenticalontilepropertiesaboutBass(Senf

5、iartin)ringsundertheconditionsoffinitegroupG—typestronglygradedrings(1GisinverseofR，eistheidentityofG)FinallytileideasofCMeninimildADelRioa】ecitedt。c。1lclude：IfR=0Rj(s=0s，)isaG(r)一typegradedri％gQ=0g吼isagEGaEF；器bigradedR—

6、S—bimoduleealdRQsdefineagradedMoritadualitybetweenRandSthenRisagradedleftBassringifandonlyifSis8gradedrightSemiartinringTilethesisisdividedinto4sectionsIllSectionlSOlllepreliminariesandnotationsarementionedIllordertobuil

7、dagoodfoundationforlatersectionsitisnecessarytocover：tilepreliminariesofgradedring；Smashproduct8’ExcellentExtensions；thebackroundofgradedBa8s(Senliarcill)rings：gradedMoritadualityectIllSection2and3gradedBass(Senliartin)r

8、ingsareintroducedandcharacterizedInSection4weconcludethatundercertaincoditionsgradedleftBassringsaredualtogradedrightSemiartinringsKeywords：GradedBassrings：GradedSemiartinrings：Smashproducts：ExcellentExtensionsofring：Gra