Abstract Algebra and Solution by Radicals

Abstract Algebra and Solution by Radicals

by John E. Maxfield, Margaret W. Maxfield
     
 

ISBN-10: 0486477231

ISBN-13: 9780486477237

Pub. Date: 04/21/2010

Publisher: Dover Publications

This advanced undergraduate-level introductory textbook first addresses groups, rings, fields and polynomials, then provides coverage of Galois theory and the proof of the unsolvability by radicals of the general equations of degree 5. With many examples, illustrations, commentaries and exercises. 13 appendices. Recommended for teacher education by The American…  See more details below

Overview

This advanced undergraduate-level introductory textbook first addresses groups, rings, fields and polynomials, then provides coverage of Galois theory and the proof of the unsolvability by radicals of the general equations of degree 5. With many examples, illustrations, commentaries and exercises. 13 appendices. Recommended for teacher education by The American Mathematical Monthly.

Product Details

ISBN-13:
9780486477237
Publisher:
Dover Publications
Publication date:
04/21/2010
Series:
Dover Books on Mathematics Series
Pages:
224
Sales rank:
770,189
Product dimensions:
6.10(w) x 9.20(h) x 0.60(d)

Related Subjects

Table of Contents

How to Use This Book
The Negative Object of This Book
Ch. 1Groups1
Discussion of the Group Properties3
Further Properties of Groups5
Examples of Groups9
Ch. 2Other Abstract Algebras18
Examples of Various Abstract Algebras20
Countable Infinity25
Equivalence and Other Relations26
Isomorphism33
Comparisons Among Abstract Algebras43
Ch. 3More About Groups47
Permutations49
Subgroups59
Congruence and Cosets62
Quotient Groups70
Ch. 4Mappings that Preserve Relations78
Ch. 5Groups of Prime Order; Two Alternating Groups88
Historical Intermission96
Some Comments on the Biographies100
Ch. 6Polynomials104
Factoring Polynomials in I[x]116
Ch. 7Algebraic Field Extensions125
Algebraic Numbers and Transcendental Numbers126
Ch. 8Galois Theory142
Ch. 9Radicals and Roots of Unity150
Ch. 10Solution by Radicals155
Appendices161
Appendix A - Q Has [actual symbol not reproducible] Members163
Appendix B - R Has [actual symbol not reproducible] Members164
Appendix C - C Has [actual symbol not reproducible] Members166
Appendix D - Graphing Complex Numbers167
Appendix E - A Lattice of Abstract Algebras173
Appendix F - Modular Arithmetic174
Appendix G - Graphical Group Representations175
Appendix H - History of Mathematics176
Appendix I - More About Field Extensions177
Appendix J - More About Galois Theory184
Appendix K - The Cyclic Group of nth Roots of Unity189
Appendix L - Proof That a Solvable Equation Has a Solvable Galois Group190
Appendix M - Impossible Constructions194
Answers to Selected Exercises199
Index205

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