代数数论

图书标准信息

• 作者 S.lang 著
• 出版社 世界图书出版公司
• 出版时间 2003-11
• 版次 2
• ISBN 9787506265621
• 定价 48.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 357页
• 正文语种 英语
• 原版书名 Algebraic Number Theory Second Edition

【内容简介】

　　ThepresentbookgivesanexpositionoftheclassicalbasicalgebraicandanalyticnumbertheoryandsupersedesmyAlgebraicNumbers,includingmuchmorematerial,e.g.theclassfieldtheoryonwhichImakefurthercommentsattheappropriateplacelater.Fordifferentpointsofview,thereaderisencouragedtoreadthecollectionofpapersfromtheBrightonSymposium(editedbyCassels-Frohlich),theArtin-Tatenotesonclassfieldtheory,WellsbookonBasicNumberTheory,Borevich-ShafarevichsNumberTheory,andalsoolderbookslikethoseofWeber,Hasse,Hecke,andHUbertsZahlbericht.Itseemsthatovertheyears,everythingthathasbeendonehasproveduseful,theoreticallyorasexamples,forthefurtherdevelopmentofthetheory.Old,andseeminglyisolatedspecialcaseshavecontinuouslyacquiredrenewedsignificance,oftenafterhalfacenturyormore.

【目录】

PartOneGeneralBasicTheory
CHAPTERIAlgebraicIntegers
1.Localization
2.Integralclosure
3.Primeideals
4.Chineseremaindertheorem
5.Galoisextensions
6.Dedekindrings
7.Discretevaluationrings
8.Explicitfaetorizationofaprime
9.ProjectivemodulesoverDedekindrings

CHAPTERII　Completions
1.Definitionsandcompletions
2.Polynomialsincompletefields
3.Somefiltrations
4.Unramifiedextensions
5.Tamelyramifiedextensions

CHAPTERIV　CyclotomicFields
1.Rootsofunity
2.Quadraticfields
3.Gausssums
4.Relationsinidealclasses

CHARTERV　Parallelotopes
1.Theproductformula
2.Latticepointsinparallelotopes
3.Avolumecomputation
4.Minkowskisconstant

CHAPTERVI　TheIdealFunction
1.Generalizedidealclasses
2.Latticepointsinhomogeneouslyexpandingdomains
3.Thenumberofidealsinagivenclass

CHAPTERVII　IdelesandAdeles
1.Restricteddirectproducts
2.Adeles
3.Ideles
4.Generalizedidealclassgroups;relationswithideleclasses
5.Embeddingofk*intheideleclasses
6.Galoisoperationonidelesandideleclasses

CHAPTER　VIII　ElementaryPropertiesoftheZetaFunctionandL-series
1.LemmasonDirichletseries
2.Zetafunctionofanumberfield
3.TheL-series
4.Densityofprimesinarithmeticprogressions
5.FaRingsfinitenesstheorem
PartTwo　ClassFieldTheory
PartThreeAnalyticTheory
Bibliography
Index