书籍 Algebraic Number Theory 作者：Lunifans 发布于 2026-06-30T13:22:57Z · 公开内容更新于 2026-10-23T09:42:54Z J.S. Milne 书籍信息 作者J.S. Milne 作者实体J.S. Milne 目录NotationIntroductionExercises1 Preliminaries from Commutative AlgebraBasic definitionsIdeals in products of ringsNoetherian ringsNoetherian modulesLocal ringsRings of fractionsThe Chinese remainder theoremReview of tensor productsExercise2 Rings of IntegersFirst proof that the integral elements form a ringDedekind's proof that the integral elements form a ringIntegral elementsReview of bases of A-modulesReview of norms and tracesReview of bilinear formsDiscriminantsRings of integers are finitely generatedFinding the ring of integersAlgorithms for finding the ring of integersExercises3 Dedekind Domains; FactorizationDiscrete valuation ringsDedekind domainsUnique factorization of idealsThe ideal class groupDiscrete valuationsIntegral closures of Dedekind domainsModules over Dedekind domains (sketch).Factorization in extensionsThe primes that ramifyFinding factorizationsExamples of factorizationsEisenstein extensionsExercises4 The Finiteness of the Class Number 进入阅读 相关 Tagalgebraic-number-theory代数数论