《抽象代数讲义》是一套久负盛名的三卷集教材，是作者雅格布斯根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的，后又成为作者《基本代数学》一书的蓝本。《抽象代数讲义（第1卷）》介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。

INTRODUCTION: CONCEPTS FROM SET THEORY THE SYSTEM OF NATURAL NUMBERS

SECTION

 1.Operationsonsets

 2.Product sets, mappings

 3.Equivalencerelations

 4.Thenaturalnumbers

 5.Thesystemofintegers

 6.The division process in I

CHAPTER I: SEMI-GROUPS AND GROUPS

 1.Definition and examples ofsemi-groups

 2.Non-associative binary compositions

 3.Generalized associativelaw.Powers

 4.Commutativity

 5.Identities andinverses

 6.Definition and examples of groups

 7.Subgroups

 8.Isomorphism

 9.Transformation groups

 10.Realization of a group as a transformation group

 II.Cyclic groups.Order of an element

 12.Elementary properties ofpermutations

 13.Coset decompositions ofa group

 14.Invariant subgroups and factor groups

 15.Homomorphismofgroups

 16.The fundamental theorem of homomorphism for groups

 17.Endomorphisms, automorphisms, center of a group

 18.Conjugatc classes

CHAPTER II: RINGS, INTEGRAL DOMAINS AND FIELDS

SECTION

 1.Definition andexamples

 2.Typesofrings

 3.Quasi-regularity.The circle composition

 4.Matrixrings

 5.Quaternions

 6.Subrings generated by a set of elements.Center

 7.Ideals, difference rings

 8.Ideals and difference rings for the ring of integers

 9.Homomorphism ofrings

 10.Anti-isomorphism

 11.Structure of the additive group of a ring.The charateristic ofaring

 12.Algebra of subgroups of the additive group of a ring.Onr sidedideals

 13.The ring of endomorphisms of a commutative group

 14.The multiplications of a ring

CHAPTER III: EXTENSIONS OF RINGS AND FIELDS

 1.Imbedding of a ring in a ring with an identity

 2.Field of fractions of a commutative integral domain

 3.Uniqueness of the field of fractions

 4.Polynomialrings

 5.Structure of polynomial rings

 6.Properties of the ring 2l[x]

 7.Simple extensions ofa field

 8.Structureofany field

 9.The number of roots of a'polynomial in a field

 10.Polynomials in several elements

 11.Symmetric polynomials

 12.Ringsoffunctions

CHAPTER IV: ELEMENTARY FACTORIZATlON THEORY

 1.Factors, associates, irreducible elements

 2.Gaussian semi-groups

 3.Greatest common divisors

 4.Principalidealdomains

SECTION

 5.Euclidean domains

 6.Polynomial extensions of Gaussian domains

CHAPTER V: GROUPS WITH OPERATORS

 1.Definition and examples.of groups with operators

 2.M-subgroups, M-factor groups and M-homomorphisms

 3.The fundamental theorem of homomorphism for M-groups

 4.The correspondence between M-subgroups determined by a homomorphism

 5.The isomorphism theorems for M-groups

 6.Schreier's theorem

 7.Simple groups and the Jordan-HSlder theorem

 8.The chain conditions

 9.Direct products

 10.Direct products of subgroups

 11.Projections

 12.Decomposition into indecomposable groups

 13.The Krull-Schmidt theorem

 14.Infinite direct products

CHAPTER VII MODULES AND IDEALS

 1.Definitions

 2.Fundamental concepts

 3.Generators.Unitary modules

 4.The chain conditions

 5.The Hilbert basis theorem

 6.Noetherian rings.Prime and primary ideals

 7.Representation of an ideal as intersection of primary ideal

 8.Uniqueness theorems

 9.Integral dependence

 10.Integers of quadratic fields

CHAPTER VII: LATTICES

 1.Partially ordered sets

 2.Lattices

 3.Modular lattices

 4.Schreier's theorem.The chain condition

SECTION

 5.Decomposition theory for lattices with ascending chain condition

 6.Independence

 7.Complemented modular lattices

 8.Boolean algebras

Index