代数(英文版) pdf epub mobi txt 电子书 下载 2025
出版者:机械工业出版社
作者:艾萨克斯 (I. Martin Isaacs)
出品人:
页数:516 页
译者:
出版时间:2003年05月
价格:65.0
装帧:平装
isbn号码:9787111119166
丛书系列:经典原版书库
图书标签:
- 代数
- 教材
- Math
- Algebra
- Mathematics
- Higher Education
- Textbook
- College
- Calculus Preparation
- Equations
- Polynomials
- Functions
- Problem Solving
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具体描述
本书系为“抽象代数”研究生课程编写的教材。 本书包含诸多代数分支主题，如有限群。环论和域论以及代数几何与模论初步等。为适应教学安排，书中题材按“非交换代数”和“交换代数”两部分组织，前一部分主要讲群论和模论基础，后一部分讲交换、域论和多项式。为便于学习，作者自然地引入基本概念和定义，并在此基础上导出相应的定理，给出严格的证明，同时举出许多例子，并在每章的结尾收入许多习题。为适应不同读者和教学内容的需求，书中还含有部分选修内容，这为那些想深入高级主题的学生提供了提高的机会，同时也便于教师按自己的风格灵活组织教学内容。
作者简介
目录信息
目录
Pt. 1 Noncommutative Algebra 1
Ch. 1 Definitions and Examples of Groups 3
Ch. 2 Subgroups and Cosets 14
Ch. 3 Homomorphisms 30
Ch. 4 Group Actions 42
Ch. 5 The Sylow Theorems and p-groups 55
Ch. 6 Permutation Groups 70
Ch. 7 New Groups from Old 83
Ch. 8 Solvable and Nilpotent Groups 99
Ch. 9 Transfer 115
Ch. 10 Operator Groups and Unique Decompositions 129
Ch. 11 Module Theory without Rings 142
Ch. 12 Rings, Ideals, and Modules 159
Ch. 13 Simple Modules and Primitive Rings 177
Ch. 14 Artinian Rings and Projective Modules 194
Ch. 15 An Introduction to Character Theory 213
Pt. 2 Commutative Algebra 231
Ch. 16 Polynomial Rings, PIDs, and UFDs 233
Ch. 17 Field Extensions 254
Ch. 18 Galois Theory 274
Ch. 19 Separability and Inseparability 293
Ch. 20 Cyclotomy and Geometric Constructions 307
Ch. 21 Finite Fields 326
Ch. 22 Roots, Radicals, and Real Numbers 342
Ch. 23 Norms, Traces, and Discriminants 359
Ch. 24 Transcendental Extensions 379
Ch. 25 The Artin-Schreier Theorem 401
Ch. 26 Ideal Theory 418
Ch. 27 Noetherian Rings 433
Ch. 28 Integrality 453
Ch. 29 Dedekind Domains 474
Ch. 30 Algebraic Sets and the Nullstellensatz 493
Index 507
· · · · · · (收起)
Pt. 1 Noncommutative Algebra 1
Ch. 1 Definitions and Examples of Groups 3
Ch. 2 Subgroups and Cosets 14
Ch. 3 Homomorphisms 30
Ch. 4 Group Actions 42
Ch. 5 The Sylow Theorems and p-groups 55
Ch. 6 Permutation Groups 70
Ch. 7 New Groups from Old 83
Ch. 8 Solvable and Nilpotent Groups 99
Ch. 9 Transfer 115
Ch. 10 Operator Groups and Unique Decompositions 129
Ch. 11 Module Theory without Rings 142
Ch. 12 Rings, Ideals, and Modules 159
Ch. 13 Simple Modules and Primitive Rings 177
Ch. 14 Artinian Rings and Projective Modules 194
Ch. 15 An Introduction to Character Theory 213
Pt. 2 Commutative Algebra 231
Ch. 16 Polynomial Rings, PIDs, and UFDs 233
Ch. 17 Field Extensions 254
Ch. 18 Galois Theory 274
Ch. 19 Separability and Inseparability 293
Ch. 20 Cyclotomy and Geometric Constructions 307
Ch. 21 Finite Fields 326
Ch. 22 Roots, Radicals, and Real Numbers 342
Ch. 23 Norms, Traces, and Discriminants 359
Ch. 24 Transcendental Extensions 379
Ch. 25 The Artin-Schreier Theorem 401
Ch. 26 Ideal Theory 418
Ch. 27 Noetherian Rings 433
Ch. 28 Integrality 453
Ch. 29 Dedekind Domains 474
Ch. 30 Algebraic Sets and the Nullstellensatz 493
Index 507
· · · · · · (收起)
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