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A First Course in Abstract Algebra,9780201335965
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A First Course in Abstract Algebra

by
Edition:
6th
ISBN13:

9780201335965

ISBN10:
0201335964
Format:
Hardcover
Pub. Date:
1/1/1999
Publisher(s):
Addison Wesley
List Price: $108.00
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Summary

Considered a classic by many, A First Course in Abstract Algebra is an in-depth, introductory text which gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The Sixth Edition continues its tradition of teaching in a classical manner, while integrating field theory and new exercises.

Table of Contents

0 A FEW PRELIMINARIES
1(30)
0.1 Mathematics and Proofs
1(6)
0.2 Sets and Relations
7(10)
0.3 Mathematical Induction
17(4)
0.4 Complex and Matrix Algebra
21(10)
1 GROUPS AND SUBGROUPS
31(62)
1.1 Binary Operations
31(12)
*Finite-State Machines (Automata)
41(2)
1.2 Isomorphic Binary Structures
43(8)
1.3 Groups
51(14)
1.4 Subgroups
65(10)
1.5 Cyclic Groups and Generators
75(18)
Cayley Digraphs
87(6)
2 MORE GROUPS AND COSETS
93(68)
2.1 Groups of Permutations
93(14)
Automata
105(2)
2.2 Orbits, Cycles, and the Alternating Groups
107(13)
Plane Isometries
117(3)
2.3 Cosets and the Theorem of Lagrange
120(8)
2.4 Direct Products and Finitely Generated Abelian Groups
128(20)
Periodic Functions
139(2)
Plane Isometries
141(7)
2.5 Binary Linear Codes
148(13)
3 HOMOMORPHISMS AND FACTOR GROUPS
161(48)
3.1 Homomorphisms
161(11)
3.2 Factor Groups
172(7)
3.3 Factor-Group Computations and Simple Groups
179(11)
3.4 Series of Groups
190(7)
3.5 Group Action on a Set
197(7)
3.6 Applications of G-Sets to Counting
204(5)
4 ADVANCED GROUP THEORY
209(44)
4.1 Isomorphism Theorems: Proof of the Jordan-Holder Theorem
209(8)
4.2 Sylow Theorems
217(7)
4.3 Applications of the Sylow Theory
224(6)
4.4 Free Abelian Groups
230(8)
4.5 Free Groups
238(6)
4.6 Group Presentations
244(9)
5 INTRODUCTION TO RINGS AND FIELDS
253(72)
5.1 Rings and Fields
253(11)
5.2 Integral Domains
264(7)
5.3 Fermat's and Euler's Theorems
271(6)
5.4 The Field of Quotients of an Integral Domain
277(8)
5.5 Rings of Polynomials
285(12)
5.6 Factorization of Polynomials over a Field
297(11)
5.7 Noncommutative Examples
308(8)
5.8 Ordered Rings and Fields
316(9)
6 FACTOR RINGS AND IDEALS
325(30)
6.1 Homomorphisms and Factor Rings
325(9)
6.2 Prime and Maximal Ideals
334(10)
6.3 Grobner Bases for Ideals
344(11)
7 FACTORIZATION
355(28)
7.1 Unique Factorization Domains
355(13)
7.2 Euclidian Domains
368(7)
7.3 Gaussian Integers and Norms
375(8)
8 EXTENSION FIELDS
383(48)
8.1 Introduction to Extension Fields
383(10)
8.2 Vector Spaces
393(9)
8.3 Algebraic Extensions
402(10)
8.4 Geometric Constructions
412(7)
8.5 Finite Fields
419(5)
8.6 Additional Algebraic Structures
424(7)
9 AUTOMORPHISMS AND GALOIS THEORY
431(64)
9.1 Automorphisms of Fields
431(10)
9.2 The Isomorphism Extension Theorem
441(7)
9.3 Splitting Fields
448(5)
9.4 Separable Extensions
453(8)
9.5 Totally Inseparable Extensions
461(4)
9.6 Galois Theory
465(9)
9.7 Illustrations of Galois Theory
474(7)
9.8 Cyclotomic Extensions
481(7)
9.9 Insolvability of the Quintic
488(7)
BIBLIOGRAPHY 495(4)
NOTATIONS 499(4)
ANSWERS TO ODD-NUMBERED EXERCISES NOT ASKING FOR DEFINITIONS OR PROOFS 503(22)
INDEX 525


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