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.

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.

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled. 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. Much algebra can be done using only very little set theory; all that is needed is a means of comparing infinite sets, and the axiom of choice in the form of Zorn's lemma.