《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3卷）》介绍域理论和伽罗瓦理论，讨论了域的代数结构和域的赋值理论。本书为全英文版本。

INTRODUCTION

SECTION

1.Extension of homomorphisms

2.Algebras

3.Tensor products of vector spaces

4.Tensor product of algebras

CHAPTER I: FINITE DIMENSIONAL EXTENSION FIELDS

1 Some vector spaces associated with mappings of fields

2.The Jacobson-Bourbaki correspondence

3.Dedekind independence theorem for isomorphisms of a field

4.Finite groups of automorphisms.

5.Splitting field of a polynomial

6.Multiple roots.Separable polynomials

7.The "fundamental theorem" of Galois theory

8.Normal extensions.Normal closures

9.Structure of algebraic extensions.Separability

10.Degrees of separability and inseparability.Structure of normal extensions

11.Primitive elements

12.Normalbases

13.Finitefields

14.Regular representation,trace and norm

15.Galois cohomology

16.Composites of fields

CHAPTER II: GALOIS THEORY OF EQUATIOIVS

1.The Galois group of an equation

2.Pureequations

3.Galois' criterion for solvability by radicals

4.The general equation of n-th degree

5.Equations with rational coefficients and symmetric group as Galoisgroup

CHAPTER Ⅲ: ABELIAN EXTENSlONS

1.Cyclotomic fields over the rationals

2.Characters of finite commutatiye groups

3.Kummer extensions

4.Witt rrectors

5.Abelian p-extensions

CHAPTER Ⅳ: STRUCTURE THEORY OF FIELDS

1 Algebraically closed fields

2.Infinite Galois theory

3.Transcendency basis

4.Luroth's theorem.

5.Linear disjointness and separating transcendency bases

6.Derivations

7.Derivations, separability and p-independence

8.Galois theory for purely inseparable extensions of exponert one

9.Higher derivations

10.Tensor products of fields

11.Free composites offields

CHAPTER V: VALUATION .THEORY

1.Realvaluations

2.Real valuations of the field of rational numbers

3.Real valuations of (x) which are trivial in

4.Completionofafield

5.Some properties of the field of p-adic numbers

6.Hensel'slemma

7.Construction of complete fields with given residue fields

8.Ordered groups and-valuations

9.Valuations, valuation rings, and places

10.Characterization of real non-archimedean valuations

11.Extension of homomorphisms and valuations

12.Application of the extension theorem: Hilbert Nullstellensatz

13.Application of the extension theorem: integral closure

SECTION

14.Finite dimensional extensions of complete fields

15.Extension of real valuations to finite dimensional extension fields

16.Ramification index and residue degree

CHAPTER VI: ARTIN-SCHREIER THEORY

1.Ordered fields and formally real fields

2.Real closed fields

3.Sturm's theorem

4.Real closure of an ordered field

5.Real algebraic numbers

6.Positive definite rational functions

7.Formalization of Sturm's theorem.Resultants

8.Decision method for an algebraic curve

9.Equations with parameters

I0.Generalized Sturm's theorem.Applications

11.Artin-Sehreier characterization of real closed fields

Suggestions for further reading

Index