An introduction to ring theory环论导论
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作者： Paul M. Cohn著
出 版 社：
出版时间： 2002-12-1字数：版次： 1页数： 229印刷时间： 2002/12/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9781852332068包装： 平装内容简介
Most parts of algebra have undergone great changes and advances in recent years, perhaps none more so than ring theory. In this volume, Paul Cohn provides a clear and structured introduction to the subject.
After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product. Tensor product and rings of fractions, followed by a description of free rings. The reader is assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
目录
Introduction
Remarks on Notation and Terminology
Chapter 1 Basics
1.1 The Definitions
1.2 Fields and Vector Spaces
1.3 Matrices
1.4 Modules
1.5 The Language of Categories
Chapter 2 Linear Algebras and Artinian Rings,
2.1 Linear Algebras
2.2 Chain Conditions
2.3 Artinian Rings: the Semisimple Case
2.4 Artinian Rings: the Radical
2.5 The Krull-Schmidt Theorem
2.6 Group Representations. Definitions and General Properties
2.7 Group Characters
Chapter 3 Noetherian Rings
3.1 Polynomial Rings
3.2 The Euclidean Algorithm
3.3 Factorization
3.4 Principal Ideal Domains
3.5 Modules over Principal Ideal Domains
3.6 Algebraic Integers
Chapter 4 PAng Constructions
4.1 The Direct Product of Rings
4.2 The Axiom of Choice and Zorn's Lemma
4.3 Tensor Products of Modules and Algebras
4.4 Modules over General Rings
4.5 Projective Modules
4.6 Injective Modules
4.7 Invariant Basis Number and Projective-Free Rings
Chapter 5 General Rings
5.1 Rings of Fractions
5.2 Skew Polynomial Rings
5.3 Free Algebras and Tensor Rings
5.4 Free Ideal Rings
Outline Solutions
Notations and Symbols
Bibliography
Index
