# Basic Algebra: Groups, Rings and Fields

Springer Science & Business Media, Dec 1, 2004 - Mathematics - 465 pages

Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic three-volume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate research students.

In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled.

The coverage is comprehensive and includes topics such as:

- Groups

- lattices and categories

- rings, modules and algebras

- fields

The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks.

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### Contents

 III 1 V 8 VI 15 VII 25 IX 32 X 34 XI 37 XII 42
 LII 238 LIII 249 LV 252 LVI 256 LVII 259 LVIII 268 LIX 272 LX 275

 XIII 46 XIV 51 XVI 60 XVII 65 XVIII 70 XIX 79 XXI 84 XXII 91 XXIII 96 XXIV 101 XXV 105 XXVI 110 XXVII 117 XXVIII 125 XXIX 131 XXXI 137 XXXII 141 XXXIII 146 XXXIV 153 XXXV 157 XXXVI 165 XXXVIII 168 XXXIX 173 XL 179 XLI 189 XLIII 195 XLIV 200 XLV 203 XLVI 206 XLVII 211 XLVIII 217 XLIX 223 L 227 LI 232
 LXI 279 LXII 291 LXIII 298 LXIV 301 LXV 307 LXVII 312 LXVIII 322 LXIX 331 LXX 336 LXXI 347 LXXIII 349 LXXIV 354 LXXV 361 LXXVI 362 LXXVII 371 LXXVIII 376 LXXIX 380 LXXX 386 LXXXI 391 LXXXII 397 LXXXIV 402 LXXXV 405 LXXXVI 409 LXXXVII 414 LXXXVIII 418 LXXXIX 427 XC 431 XCI 437 XCII 441 XCIII 449 XCIV 453 XCV 457 XCVI 459 Copyright