代數(英文版) pdf epub mobi txt 電子書 下載2025
出版者:機械工業齣版社
作者:艾薩剋斯 (I. Martin Isaacs)
出品人:
頁數:516 页
译者:
出版時間:2003年05月
價格:65.0
裝幀:平裝
isbn號碼:9787111119166
叢書系列:經典原版書庫
圖書標籤:
- 代數
- 教材
- Math
- Algebra
- Mathematics
- Higher Education
- Textbook
- College
- Calculus Preparation
- Equations
- Polynomials
- Functions
- Problem Solving
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具體描述
本書係為“抽象代數”研究生課程編寫的教材。 本書包含諸多代數分支主題，如有限群。環論和域論以及代數幾何與模論初步等。為適應教學安排，書中題材按“非交換代數”和“交換代數”兩部分組織，前一部分主要講群論和模論基礎，後一部分講交換、域論和多項式。為便於學習，作者自然地引入基本概念和定義，並在此基礎上導齣相應的定理，給齣嚴格的證明，同時舉齣許多例子，並在每章的結尾收入許多習題。為適應不同讀者和教學內容的需求，書中還含有部分選修內容，這為那些想深入高級主題的學生提供瞭提高的機會，同時也便於教師按自己的風格靈活組織教學內容。
著者簡介
圖書目錄
目錄
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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