Dummit《Abstract Algebra Third Edition 》Ⅰ

4.5 SYLOW'S THEOREM 4.5 西洛定理 In this section we prove a partial converse to Lagrange’s Theorem and d

5.1 DIRECT PRODUCTS 5.1 直接积 We begin with the definition of the direct product of a finite and of a

5.2 THE FUNDAMENTAL THEOREM OF FINITELY GENERATED ABELIAN GROUPS 5.2 有限生成阿贝尔群的基本定理 Definition. 定义。 (

5.3 TABLE OF GROUPS OF SMALL ORDER 5.3 小阶群的表格 At this point we can give a table of the isomorphism t

5.5 SEMIDIRECT PRODUCTS 5.5 半直积 In this section we study the "semidirect product" of two groups $H$

6.1 $p$ -GROUPS,NILPOTENT GROUPS,AND SOLVABLE GROUPS 6.1 $p$ -群，幂零群和可解群 Let $p$ be a prime and let $

6.2 APPLICATIONS IN GROUPS OF MEDIUM ORDER 6.2 中等阶群中的应用 The purpose of this section is to work throu

6.3 A WORD ON FREE GROUPS 6.3 关于自由群的讨论 In this section we introduce the basic theory of so-called fr

7.1 BASIC DEFINITIONS AND EXAMPLES 7.1 基本定义和例子 Definition. 定义。 (1) A ring $R$ is a set together with

7.2 EXAMPLES: POLYNOMIAL RINGS, MATRIX RINGS, AND GROUP RINGS 7.2 示例：多项式环，矩阵环和群环 We introduce here t

7.3 RING HOMOMORPHISMS AND QUOTIENT RINGS 7.3 环同态与商环 A ring homomorphism is a map from one ring to a

7.4 PROPERTIES OF IDEALS 7.4 理想的性质 Throughout this section $R$ is a ring with identity $1 \neq 0$ .

7.5 RINGS OF FRACTIONS 7.5 分式环 Throughout this section $R$ is a commutative ring. Proposition 2 show

7.6 THE CHINESE REMAINDER THEOREM 7.6 中国剩余定理 Throughout this section we shall assume unless otherwis

8.1 EUCLIDEAN DOMAINS 8.1 欧几里得域 We first define the notion of a norm on an integral domain $R$ . Thi

8.2 PRINCIPAL IDEAL DOMAINS (P.I.D.s ) 8.2 主理想整环（P.I.D.s） Definition. A Principal Ideal Domain (P.I.

8.3 UNIQUE FACTORIZATION DOMAINS (U.F.D.s ) 8.3 唯一分解整环 (U.F.D.s) In the case of the integers $\mathb

9.1 DEFINITIONS AND BASIC PROPERTIES 9.1 定义与基本性质 The polynomial ring $R\left\lbrack x\right\rbrack$

9.2 定义在域上的多项式环 I We now consider more carefully the situation where the coefficient ring is a field

9.3 POLYNOMIAL RINGS THAT ARE UNIQUE FACTORIZATION DOMAINS 9.3 是唯一分解整环的多项式环 We have seen in Proposit