A First Course in Abstract Algebra
ISBN: 9780201763904 | 0201763907
Edition: 7thFormat: Hardcover
Publisher: Pearson
Pub. Date: 11/6/2002
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Considered a classic by many,A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permut... MORE
| Instructor's Preface | vii | ||||
| Student's Preface | xi | ||||
| Dependence Chart | xiii | ||||
| 1 | (10) | |||
| I Groups and Subgroups | ... MORE | (64) | |||
| 11 | (9) | |||
| 20 | (8) | |||
| 28 | (8) | |||
| 36 | (13) | |||
| 49 | (10) | |||
| 59 | (9) | |||
| 68 | (7) | |||
| II Permutations, Cosets, and Direct Products | 75 | (50) | |||
| 75 | (12) | |||
| 87 | (9) | |||
| 96 | (8) | |||
| 104 | (10) | |||
| 114 | (11) | |||
| III Homomorphisms and Factor Groups | 125 | (42) | |||
| 125 | (10) | |||
| 135 | (9) | |||
| 144 | (10) | |||
| 154 | (7) | |||
| 161 | (6) | |||
| IV Rings and Fields | 167 | (70) | |||
| 167 | (10) | |||
| 177 | (7) | |||
| 184 | (6) | |||
| 190 | (8) | |||
| 198 | (11) | |||
| 209 | (11) | |||
| 220 | (7) | |||
| 227 | (10) | |||
| V Ideals and Factor Rings | 237 | (28) | |||
| 237 | (8) | |||
| 245 | (9) | |||
| 254 | (11) | |||
| VI Extension Fields | 265 | (42) | |||
| 265 | (9) | |||
| 274 | (9) | |||
| 283 | (10) | |||
| 293 | (7) | |||
| 300 | (7) | |||
| VII Advanced Group Theory | 307 | (48) | |||
| 307 | (4) | |||
| 311 | (10) | |||
| 321 | (6) | |||
| 327 | (6) | |||
| 333 | (8) | |||
| 341 | (5) | |||
| 346 | (9) | |||
| VIII Groups in Topology | 355 | (34) | |||
| 355 | (8) | |||
| 363 | (8) | |||
| 371 | (8) | |||
| 379 | (10) | |||
| IX Factorization | 389 | (26) | |||
| 389 | (12) | |||
| 401 | (6) | |||
| 407 | (8) | |||
| X Automorphisms and Galois Theory | 415 | (62) | |||
| 415 | (9) | |||
| 424 | (7) | |||
| 431 | (5) | |||
| 436 | (8) | |||
| 444 | (4) | |||
| 448 | (9) | |||
| 457 | (7) | |||
| 464 | (6) | |||
| 470 | (7) | |||
| Appendix: Matrix Algebra | 477 | (6) | |||
| Bibliography | 483 | (4) | |||
| Notations | 487 | (4) | |||
| Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs | 491 | (22) | |||
| Index | 513 |
