Basic Algebra : Groups, Rings and Fields

**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. Front Matter....Pages i-xii Sets....Pages 1-23 Groups....Pages 25-50 Lattices and Categories....Pages 51-78 Rings and Modules....Pages 79-130 Algebras....Pages 131-163 Multilinear Algebra....Pages 165-188 Field Theory....Pages 189-248 Quadratic Forms and Ordered Fields....Pages 249-306 Valuation Theory....Pages 307-345 Commutative Rings....Pages 347-396 Infinite Field Extensions....Pages 397-447 Back Matter....Pages 449-465 Preface Conventions on Terminology Sets Groups Lattices and Categories Rings and Modules Algebras Multilinear Algebra Field Theory Quadratic Forms and Ordered Fields Valuation Theory Commutative Rings Infinite Field Extensions Bibliography List of Notations Author Index Subject Index.