伽罗瓦环的高斯扩张和四元数扩张.pdf

《伽罗瓦环的高斯扩张和四元数扩张.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ChineseAbstract³³³ÛÛÛ‚‚‚pppddd***ÜÜÜÚÚÚoooêêê***ÜÜÜÁÁÁ‡‡‡k•‚´“êÆ¥•Ä•´••‡ïÄé–ƒ˜§‚Ø¥Nõ(ØÑ´d§í25"§†+Ø!‰Æ!

2、ÜêÆ!ÿÀÆ!ãدõêÆ©

3、kXéX;—§¿3ó§‰ÆÚÏ&‰Æ+•¥kX•‡A^"AO´Cn›c±5§duOŽÅEâ9péuЧ?ènØuЛ©×„§l•?˜ÚíÄk•‚ïÄ"³Û‚GR(pn;r)´˜aš~•‡k•‚§§´k•ÛÜ‚Zpn³Û*ܧ•´k••Fpr•‡í2"éõÆöé³Û‚?1ïħ¿òÙ2•A^k••¤

4、A^+•"©̇ïÄé–´³Û‚pd*ÜÚoê*Ü"Äk31˜ÙpVãïĵ±9³Û‚½Â9ƒ'5Ÿ§¿‰Ñ©Ù¥Ñyk•‚Úk••þ˜ÄVgÚ(Ø"31Ù·‚̇•Ä³Û‚pd*Ü"1˜!̇ïÄ¿(½³Û‚pd*Ü4ŒnŽ!_ŽÙÜŠÚƒÌ"31!p§·‚‰ÑÙ̇(؃˜µ³Û‚pd*Üü+(½n"^ãØóäïÄ“ê(´•C20c5â)˜‡#.ïÄ+•§ÚuÑéõk(JÚ¯K"3Ù1n!p§·‚̇ïijÛ‚pd*Ü"Ïfã˜5Ÿ§(½"Ïfãdaã"AO/§•x"Ïfㆻڌ•§¿…‰Ñ§´²¡ã

5、¿‡^‡"Ù1o!p§·‚‰Ñ˜‡ò³Û‚þ½nJ,³Û‚pd*Üþ~f"•31nÙ¥·‚•Ä³Û‚oê*Ü"ïħü>9V>nŽ(§(½§"Ïf§ƒÌ§_ŽÙÜŠ±9ü+("'''………ccc:³Û‚;"Ïf;_ŽÙÜŠ;pd*Ü;oê*ÜiEnglishAbstractTheGaussianExtensionandQuaternionExtensionofaGaloisRingAbstractFiniteringsareoneofbasicandimportantsubjectsinalgebra;manyresultsinringtheoryar

6、egeneralizedthoseinniterings.Itiscloselyrelativewithmanybranchesofmathematics,suchasgrouptheory,modulecategory,combinatorics,topology,andgraphtheory.Ithassignicantapplicationsinengineeringscienceandcommunicationscience.Especiallyinthelast30years,withthedevelopmentofcomputertechnologyandtheinter

7、net,andthequickdevelopmentofcodingtheory,thestudyofniteringsarefurtherpromoted.TheGaloisringGR(pn;r)isoneofimportantniterings;itisaGaloisextensionofthenitelocalringZpnandthegeneralizationoftheniteeldFpr.ManyscholarsstudiedGaloisrings,andwidelyappliedtothoseofniteeldsappliedto.Thesubjectmat

8、terofthisthesisistostudyGaussianextensionsandquaternionextensionsofGaloisrings.Werstsummarizetheresearchbackground,andgivedenitionandsomebasicpropertiesofGaloisrings.Wealsopresentsomebasicconceptsandfactsinniteringsandniteeldswhichappearinthisarticle.InChapter2,wemainlystudytheGaussianextens

9、ionsofGaloisrings.Intherstsection,westudyandndthemaximalideals,theJacobsonradicalandprimespectrumoftheGaussianextensionsofGaloisrings.Oneofmainresultsinthischapterwillbefoundinthesectiontwo.Wedeterminetheunitgroupstr