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· 제목 : Algebraic Number Theory (Hardcover, 2)
· 분류 : 외국도서 > 컴퓨터 > 운영체제(OS) > 일반
· ISBN : 9781439845981
· 쪽수 : 442쪽
· 출판일 : 2011-01-05
· 분류 : 외국도서 > 컴퓨터 > 운영체제(OS) > 일반
· ISBN : 9781439845981
· 쪽수 : 442쪽
· 출판일 : 2011-01-05
목차
Integral Domains, Ideals, and Unique Factorization
Integral Domains
Factorization Domains
Ideals
Noetherian and Principal Ideal Domains
Dedekind Domains
Algebraic Numbers and Number Fields
Quadratic Fields
Field Extensions
Automorphisms, Fixed Points, and Galois Groups
Norms and Traces
Integral Bases and Discriminants
Norms of Ideals
Class Groups
Binary Quadratic Forms
Forms and Ideals
Geometry of Numbers and the Ideal Class Group
Units in Number Rings
Dirichlet’s Unit Theorem
Applications: Equations and Sieves
Prime Power Representation
Bachet’s Equation
The Fermat Equation
Factoring
The Number Field Sieve
Ideal Decomposition in Number Fields
Inertia, Ramification, and Splitting of Prime Ideals
The Different and Discriminant
Ramification
Galois Theory and Decomposition
Kummer Extensions and Class-Field Theory
The Kronecker?Weber Theorem
An Application?Primality Testing
Reciprocity Laws
Cubic Reciprocity
The Biquadratic Reciprocity Law
The Stickelberger Relation
The Eisenstein Reciprocity Law
Appendix A: Abstract Algebra
Appendix B: Sequences and Series
Appendix C: The Greek Alphabet
Appendix D: Latin Phrases
Bibliography
Solutions to Odd-Numbered Exercises
Index
