TAILIEUCHUNG - ALGEBRAIC NUMBER THEORY

Tham khảo sách 'algebraic number theory', kinh doanh - tiếp thị, quản trị kinh doanh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ALGEBRAIC NUMBER THEORY Edited by I Co wk A Frthllch ALGEBRAIC NUMBER THEORY . MILNE Abstract. These are the notes for a course taught at the University of Michigan in F92 as Math 676. They are available at jmilne . Please send comments and corrections to me at jmilne@. August 14 1996. First version on the web. August 31 1998. Fixed many minor errors added exercises and index. Contents The ring of integers 1 Factorization 2 Units 4 Applications 5 A brief history of numbers 6 References. 7. 1. Preliminaries from Commutative Basic definitions 10 Noetherian rings 10 Local rings 12 Rings of fractions 12 The Chinese remainder theorem 14 Review of tensor products 15 Extension of scalars 17 Tensor products of algebras 17 Tensor products of fields 17. 2. Rings of Symmetric polynomials 19 Integral elements 20 Review of bases of A-modules 25 Review of norms and traces 25 Review of bilinear forms 26 Discriminants 26 Rings of integers are finitely generated 28 Finding the ring of integers 30 Algorithms for finding the ring of integers 33. 3. Dedekind Domains Discrete valuation rings 37 Dedekind domains 38 Unique factorization 39 The ideal class group 43 Discrete valuations 46 Integral closures of Dedekind domains 47 Modules over Dedekind domains sketch . 48 Factorization in extensions 49 The primes that ramify 50 Finding factorizations 53 Examples of factorizations 54 Eisenstein extensions 56. 4. The Finiteness of the Class Norms of ideals 58 Statement of the main theorem and its consequences 59 Lattices 62 Some calculus 67 Finiteness of the class number 69 Binary quadratic forms 71 5. The Unit Statement of the theorem 73 Proof that UK is finitely generated 74 Computation of the rank 75 S-units 77 Finding fundamental units in real @1996 1998 . Milne. You may make one copy of these notes for your own personal use. i 0 . MILNE quadratic fields 77 .

• Quản trị kinh doanh
• Iterated integrals
• Line integrals
• Periodic functions
• The Fourier integral
• ALGEBRAIC NUMBER THEORY
• definite integral
• Vectors
• improper integral
• Techniques
• discrete steps
• To infinity
• Complex number
• Improper integrals
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• Random permutation σ
• Prime numbers
• Distinct residue classes modulo
• Algebraic number fields
• Number theory