 | ||||||||||||||||
| ||||||||||||||||
by Allan Clark
|
ISBN: 0486647250 Dover Publications Price: $12.95 |
click here to see this book |
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.
Reprint of the 1971 edition.
Table of Contents for Elements of Abstract Algebra
| Foreword; Introduction | |||||||
| I. Set Theory | |||||||
| 1-9. The notation and terminology of set theory | |||||||
| 10-16. Mappings | |||||||
| 17-19. Equivalence relations | |||||||
| 20-25. Properties of natural numbers | |||||||
| II. Group Theory | |||||||
| 26-29. Definition of group structure | |||||||
| 30-34. Examples of group structure | |||||||
| 35-44. Subgroups and cosets | |||||||
| 45-52. Conjugacy, normal subgroups, and quotient groups | |||||||
| 53-59. The Sylow theorems | |||||||
| 60-70. Group homomorphism and isomorphism | |||||||
| 71-75. Normal and composition series | |||||||
| 76-86. The Symmetric groups | |||||||
| III. Field Theory | |||||||
| 87-89. Definition and examples of field structure | |||||||
| 90-95. Vector spaces, bases, and dimension | |||||||
| 96-97. Extension fields | |||||||
| 98-107. Polynomials | |||||||
| 108-114. Algebraic extensions | |||||||
| 115-121. Constructions with straightedge and compass | |||||||
| IV. Galois Theory | |||||||
| 122-126. Automorphisms | |||||||
| 127-138. Galois extensions | |||||||
| 139-149. Solvability of equations by radicals | |||||||
| V. Ring Theory | |||||||
| 150-156. Definition and examples of ring structure | |||||||
| 157-168. Ideals | |||||||
| 169-175. Unique factorization | |||||||
| VI. Classical Ideal Theory | |||||||
| 176-179. Fields of fractions | |||||||
| 180-187. Dedekind domains | |||||||
| 188-191. Integral extensions | |||||||
| 192-198. Algebraic integers | |||||||
| Bibliography; Index |