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Algebra(代数 第3版) 版权信息
- ISBN:9787519255756
- 条形码:9787519255756 ; 978-7-5192-5575-6
- 装帧:简裝本
- 册数:暂无
- 重量:暂无
- 所属分类:>>
Algebra(代数 第3版) 内容简介
本书是一部很有影响力的研究生教材,全面介绍了代数的基本概念。本书的突出特点是书中不但保留了代数的经典内容,同时也介绍了从 范畴理论和同调代数思考的学习方式,各章有大量习题。本书可做为研究生教材,学时一年。
Algebra(代数 第3版) 目录
Part One The Basic Objects of Algebra
Chapter I Groups
1. Monoids
2. Groups
3. Normal subgroups
4. Cyclic groups
5. Operations of a group on a set
6. Sylow subgroups
7. Direct sums and free abelian groups
8. Finitely generated abelian groups
9. The dual group
10. Inverse limit and completion
11. Categories and functors
12. Free groups
Chapter II Rings
1. Rings and homomorphisms
2. Commutative rings
3. Polynomials and group rings
4. Localization
5. Principal and factorial rings
Chapter III Modules
1. Basic definitions
2. The group of homomorphisms
3. Direct products and sums of modules
4. Free modules
5. Vector spaces
6. The dual space and dual module
7. Modules over principal rings
8. Euler-Poincare maps
9. The snake lemma
10. Direct and inverse limits
Chapter IV Polynomials
1. Basic properties for polynomials in one variable
2. Polynomials over a factorial ring
3. Criteria for irreducibility
4. Hilbert's theorem
5. Partial fractions
6. Symmetric polynomials
7. Mason-Stothers theorem and the abe conjecture
8. The resultant
9. Power series
Part Two Algebraic Equations
Chapter V Algebraic Extensions
1. Finite and algebraic extensions
2. Algebraic closure
3. Splitting fields and normal extensions
4. Separable extensions
5. Finite fields
6. Inseparable extensions
Chapter VI Galois Theory
1. Galois extensions
2. Examples and applications
3. Roots of unity
4. Linear independence of characters
5. The norm and trace
6. Cyclic extensions
7. Solvable and radical extensions
8. Abelian Kummer theory
9. The equation X\
Chapter I Groups
1. Monoids
2. Groups
3. Normal subgroups
4. Cyclic groups
5. Operations of a group on a set
6. Sylow subgroups
7. Direct sums and free abelian groups
8. Finitely generated abelian groups
9. The dual group
10. Inverse limit and completion
11. Categories and functors
12. Free groups
Chapter II Rings
1. Rings and homomorphisms
2. Commutative rings
3. Polynomials and group rings
4. Localization
5. Principal and factorial rings
Chapter III Modules
1. Basic definitions
2. The group of homomorphisms
3. Direct products and sums of modules
4. Free modules
5. Vector spaces
6. The dual space and dual module
7. Modules over principal rings
8. Euler-Poincare maps
9. The snake lemma
10. Direct and inverse limits
Chapter IV Polynomials
1. Basic properties for polynomials in one variable
2. Polynomials over a factorial ring
3. Criteria for irreducibility
4. Hilbert's theorem
5. Partial fractions
6. Symmetric polynomials
7. Mason-Stothers theorem and the abe conjecture
8. The resultant
9. Power series
Part Two Algebraic Equations
Chapter V Algebraic Extensions
1. Finite and algebraic extensions
2. Algebraic closure
3. Splitting fields and normal extensions
4. Separable extensions
5. Finite fields
6. Inseparable extensions
Chapter VI Galois Theory
1. Galois extensions
2. Examples and applications
3. Roots of unity
4. Linear independence of characters
5. The norm and trace
6. Cyclic extensions
7. Solvable and radical extensions
8. Abelian Kummer theory
9. The equation X\
展开全部
Algebra(代数 第3版) 作者简介
本书作者S.朗(S. Lang)是美国耶鲁大学教授,撰写的经典教材学术著作等身,《代数》是作者的代表作之一,堪称数学领域的经典教材。
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