《代數數論講義》是世界圖書出版公司2000年出版的圖書，由黑克（Erich Hecke）編著。
基本介紹
- 作者：Erich Hecke
- ISBN：9787506201070
- 頁數：239
- 定價：37.00元
- 出版社：世界圖書出版公司
- 出版時間：2000-12
- 裝幀：平裝
- 叢書： Graduate Texts in Mathematics
內容介紹,目錄,
內容介紹
Hecke was certainly one of the masters, and in fact, the study of Hecke Lseries and Hecke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book,and Hecke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Hecke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task."
目錄
CHAPTER Ⅰ Elements of Rational Number Theory
1. Divisibility, Greatest Common Divisors, Modules, Prime Numbers, and the Fundamental Theorem of Number Theory Theorems 1-5
2. Congruences and Residue Classes Euler''sfunction （n）.Ferrnat'' s theorem. Theorems 6-9
3. Integral Polynomials, Functional Congruences, and Divisibility mod p Theorems lO-13a
4. Congruences of the First Degree Theorems 14-15
CHAPTER Ⅱ Abelian Groups
5. The General Group Concept and Calculation with Elements of a Group Theorems 16-18
6. Subgroups and Division of a Group by a Subgroup Order of elements. Theorems 19-21
7. Abelian Groups and the Product of Two Abeliun Groups Theorems 22-25
8. Basis of an Abelian Group The basis number ora group belonging to a prime number. Cyclic groups. Theorems 26-28
9. Composition of Cosets and the Factor Group Theorem 29
10. Characters of Abelian Groups The group of characters. Determination of all subgroups. Theorems 30-33
11. Infinite Abelian Groups Finite basis of such a group and basis for a subgroup. Theorems 34-40
CHAPTER Ⅲ Abelian Groups in Rational Number Theory
12. Groups of Integers under Addition and Multiplication Theorem 41
1. Divisibility, Greatest Common Divisors, Modules, Prime Numbers, and the Fundamental Theorem of Number Theory Theorems 1-5
2. Congruences and Residue Classes Euler''sfunction （n）.Ferrnat'' s theorem. Theorems 6-9
3. Integral Polynomials, Functional Congruences, and Divisibility mod p Theorems lO-13a
4. Congruences of the First Degree Theorems 14-15
CHAPTER Ⅱ Abelian Groups
5. The General Group Concept and Calculation with Elements of a Group Theorems 16-18
6. Subgroups and Division of a Group by a Subgroup Order of elements. Theorems 19-21
7. Abelian Groups and the Product of Two Abeliun Groups Theorems 22-25
8. Basis of an Abelian Group The basis number ora group belonging to a prime number. Cyclic groups. Theorems 26-28
9. Composition of Cosets and the Factor Group Theorem 29
10. Characters of Abelian Groups The group of characters. Determination of all subgroups. Theorems 30-33
11. Infinite Abelian Groups Finite basis of such a group and basis for a subgroup. Theorems 34-40
CHAPTER Ⅲ Abelian Groups in Rational Number Theory
12. Groups of Integers under Addition and Multiplication Theorem 41
