Abstract algebra : a concrete introduction

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Title:

Personal Author:

Redfield, Robert H.

Publication Information:

Boston : Longman, 2000

ISBN:

9780201437218

Subject Term:

Algebra, Abstract

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004568436	QA162 R43 2000	Open Access Book	Book	Searching... Unknown

This is a new text for the Abstract Algebra course. The author has written this text with a unique, yet historical, approach: solvability by radicals. This approach depends on a fields-first organization. However, professors wishing to commence their course with group theory will find that the Table of Contents is highly flexible, and contains a generous amount of group coverage.

Introduction	p. xvii
Historical Note: Al-Khwarizmi	p. xix
Part 1 Preliminaries	p. 1
Chapter 1 Properties of the Integers	p. 3
Historical Note: Augustus de Morgan	p. 16
Chapter 2 Solving Cubic and Quartic Polynomial Equations	p. 18
Historical Note: How the Cubic and Quartic Equations Were Solved	p. 31
Chapter 3 Complex Numbers	p. 34
Historical Note: Highlights in the Development of the Complex Numbers	p. 48
Chapter 4 Some Other Examples	p. 58
Historical Note: William Rowan Hamilton	p. 66
Part 2 Algebraic Extension Fields	p. 69
Chapter 5 Fields	p. 70
Chapter 6 Solvability by Radicals	p. 81
Historical Note: Niels Henrik Abel	p. 91
Chapter 7 Rings	p. 95
Chapter 8 Ways in Which Polynomials Are Like the Integers	p. 103
Historical Note: Julia Robinson	p. 116
Chapter 9 Principal Ideals	p. 119
Historical Note: Emmy Noether	p. 127
Chapter 10 Algebraic Elements	p. 130
Chapter 11 Eisenstein's Irreducibility Criterion	p. 140
Historical Note: Gotthold Eisenstein	p. 146
Chapter 12 Extension Fields as Vector Spaces	p. 148
Chapter 13 Automorphisms to Fields	p. 159
Historical Note: Evariste Galois	p. 167
Chapter 14 Counting Automorphisms	p. 170
Historical Note: Richard Dedekind	p. 180
Part 3 Elementary Group Theory	p. 183
Chapter 15 Groups	p. 184
Historical Note: Walther von Dyck	p. 194
Chapter 16 Permutation Groups	p. 196
Chapter 17 Group Homomorphisms	p. 203
Historical Note: Arthur Cayley	p. 209
Chapter 18 Subgroups	p. 211
Chapter 19 Subgroups Generated by Subsets	p. 220
Chapter 20 Cosets	p. 226
Chapter 21 Finite Groups and Lagrange's Theorem	p. 233
Historical Note: Joseph Louis Lagrange	p. 241
Chapter 22 Equivalence Relations and Cauchy's Theorem	p. 243
Historical Note: Augustin-Louis Cauchy	p. 251
Chapter 23 Normal Subgroups and Quotient Groups	p. 254
Historical Note: Otto Holder	p. 259
Chapter 24 The Homomorphism Theorem for Groups	p. 262
Historical Note: B. L. van der Waerden	p. 268
Part 4 Polynomial Equations Not Solvable by Radicals	p. 271
Chapter 25 Galois Groups of Radical Extensions	p. 272
Chapter 26 Solvable Groups and Commutator Subgroups	p. 280
Historical Note: William Burnside	p. 287
Chapter 27 Solvable Galois Groups	p. 288
Chapter 28 Polynomial Equations Not Solvable by Radicals	p. 296
Historical Note: Paolo Ruffini	p. 299
Part 5 Finite Groups	p. 301
Chapter 29 Finite External Direct Products of Groups	p. 302
Historical Note: J. H. M. Wedderburn	p. 310
Chapter 30 Finite Internal Direct Products of Groups	p. 312
Chapter 31 Abelian Groups with Prime Power Order	p. 320
Chapter 32 The Fundamental Theorem of Finite Abelian Groups	p. 329
Historical Note: Leopold Kronecker	p. 337
Chapter 33 Dihedral Groups	p. 339
Historical Note: Felix Klein	p. 345
Chapter 34 Cauchy's Theorem	p. 348
Chapter 35 The Sylow Theorems	p. 359
Historical Note: Peter Ludvig Sylow	p. 370
Chapter 36 Groups of Order Less Than 16	p. 372
Chapter 37 Groups of Even Permutations	p. 380
Historical Note: Camille Jordan	p. 386
Chapter 38 Semidirect Products	p. 388
Appendix A The Greek Alphabet	p. 396
Appendix B Proving Theorems	p. 397
Historical Note: George Boole	p. 410
Appendix C Vector Spaces Over Fields	p. 413
Appendix D Constructions with Straightedge and Compass	p. 418
Answers to Odd-Numbered Computational Exercises	p. 426
Bibliography	p. 444
Photo Credits	p. 446
Notation Index	p. 447
Subject Index	p. 448

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