20432.k[x1,x2x11,x21]上的分次擴張

1、K㈨z2：X～17zi1]上的分次擴張專業(yè)名稱：基礎數(shù)學申請人：孟淑慧指導教師：謝光明教授論文答辯委員會主席委員：廣西師范大學碩士學位論文Kpl2“2：zf3：zil]上的分次擴張GradedExtensionsin／([Zl，x2；X～1，zi1]Author：MengShuhuiSupervisor：XieGuangmingMajor：FundamentalMathematicsSpeciality：AlgebraGrade：201

2、2ABSTRACTAsanimportantclassofringsnon—commutativevaluationringsaleofgreatsignificanceintheresearchofnon—commutativeringtheoryRingextensionisanimportantpartofringtheoryAttheendoflastcenturythequestionofnon—commutativevalu

3、ationringextensionsWasputforwardbyHHBrungs，GTSrnerandMSchrSderAfterthat，nmchimportantprogresshasbeenobtainedGradedextensionsandGaussextensionsaretwokindsofimportantvaluationringextensions，andthereisaonetoonecorrespondenc

4、ebetweengradedextensionsandGaussextensionsSoitsufhcestostudygradedextensionsinordertostudyGaussextensionsSkewLaurentpolynomialringisanimportantclassofringGradedextensionsinskewLanrentpolynomialringK[x，X1；盯]andtrivialgrad

5、edextensionsinskewgroupringK[Z2；盯]werediscussedindetailbyGuangmingXieetc，wherezistheadditivegroupofintegers，Aut(K)isthegroupofautomorphismsofdivisionringKandOisagrouphomomorphismfromZ2toAut(K)Butforextensionsinskewgroupr

6、ingK[Z2；仃]，however，onlythesimplesttrivialgradedextensionswerediscussedGeneralgradedextensionswerenotWewillgiveacompleteclassificationofgradedextensionsinK[xl，x2；z_1，zil]，anddescribethestructuresofeachtypeindetailInthisth

7、esis，gradedextensionsinK[Xl，zfl】andK[x2，zil]aregivenWewilldiscusstheexistenceanduniquenessofgradedextensionsinK[xl，X2；zfl，zil]WewillalsodescribetheconcretestructuresofgradedextensionsinK[zl，x2；zfl，zil]Atlast，wewillgiveso

8、meexamplesofeachtypeThisthesisiscomposedoffourpartsThefirstpartthirdpartarethemainbodiesofthisthesisAndthelastiSintroductionThesecondandpartistheconcludingremarksInChapterl，someoftheresearchbackground，researchsignificanc

9、eandmainresultsareintroducedInChapter2，wewillgiveacompleteclassificationofgradedextensionsinK[xl，x2；zfl，zil]，anddescribethestructuresofeachtypeindetailTheresultsinthissectionwerepublishedinJournalofGuangxiNormalUniversit