Dummit《Abstract Algebra Third Edition 》Ⅰ

9.4 IRREDUCIBILITY CRITERIA 9.4 不可约性准则 If $R$ is a Unique Factorization Domain,then by Corollary 8 a

9.5 POLYNOMIAL RINGS OVER FIELDS II 9.5 多项式环在域上的 II Let $F$ be a field. We prove here some additiona

9.6 POLYNOMIALS IN SEVERAL VARIABLES OVER A FIELD AND GRÖBNER BASES 9.6 多元多项式在域上的运算和格罗布纳基 In this se

Gröbner Bases and Solving Algebraic Equations: Elimination Gröbner基与代数方程求解：消元 The theory of Gröbner

10.1 BASIC DEFINITIONS AND EXAMPLES 10.1 基本定义与示例 We start with the definition of a module. 我们从模的定义开始

10.2 QUOTIENT MODULES AND MODULE HOMOMORPHISMS 10.2 商模块与模块同态 This section contains the basic theory

10.3 GENERATION OF MODULES, DIRECT SUMS, AND FREE MODULES 10.3 模的生成，直和与自由模 Let $R$ be a ring with 1

10.4 TENSOR PRODUCTS OF MODULES 10.4 模的张量积 在这一节中，我们研究两个模 $M$ 和 $N$ 在包含 1 的环（不一定是交换环）上的张量积。张量积的形成是一种通

10.5 EXACT SEQUENCES—PROJECTIVE, INJECTIVE, AND FLAT MODULES 研究代数对象 $B$（例如，群、环或模块）结构的基本结果之一是第一同构定理，该

Injective Modules and ${\operatorname{Hom}}_{R}\left( {_ _ ,D}\right)$ 注射模块和 ${\operatorname{Hom}}_{

12.1 THE BASIC THEORY 12.1 基础理论 We first describe some general finiteness conditions. Let $R$ be a r

12.2 THE RATIONAL CANONICAL FORM 12.2 有理标准形 We now apply our results on finitely generated modules i

12.3 THE JORDAN CANONICAL FORM 12.3 约当标准形 We continue with the notation in the previous section: $F$