基础代数

Preface

Conventions on Terminology

1.Sets

2.Groups

3.Lattices and Categories

4.Rings and Modules

5.Algebras

6.Multilinear Algebra

7.Field Theory

8.Quadratic Forms and Ordered Fields

9.Valuation Theory

10.Commutative Rings

11.Infinite Field Extensions

Bibliography

List of Notations

Author Index

Subject Index

Apart from chapters on groups (Chapter 2), rings and modules (Crhapters 4, 5 and 6) and fields (Chapters 7 and 11), a number of concepts are treated that are less central but nevertheless have many uses. Chapter 1, on set theory, deals with countable and well-ordered sets, as weU as Zorn's lemma and a brief section on graphs. Chapter 3 introduces lattices and categories, both concepts that form an important part of the language of modern algebra. The general theory of quadratic forms has many links with ordered fields, which are developed in Chapter 8. Chapters 9 and 10 are devoted to valuation theory and commutative rings, a subject that has gained in importance through its use in algebraic geometry.

《基础代数》是P. M. Cohn的经典的三卷集代数教材的修订版第一卷，被广大读者所追捧，公认为学习代数入门教材的杰出代表。《基础代数》中涵盖了代数的所有重要结果。读者具备一定的线性代数、群和域知识，对理解本书将更有益。本卷次的目次：集合；群；格点和范畴；环和模；代数；多线性代数；域论；二次型和有序域；赋值论；交换环；无限域扩展。
　　《基础代数》读者对象：数学专业的广大师生。