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Algebra I

Textbook for Students of Mathematics

  • Alexey L. Gorodentsev

Table of contents

  1. Front Matter
    Pages i-xx
  2. Alexey L. Gorodentsev
    Pages 1-18
  3. Alexey L. Gorodentsev
    Pages 19-40
  4. Alexey L. Gorodentsev
    Pages 41-71
  5. Alexey L. Gorodentsev
    Pages 73-102
  6. Alexey L. Gorodentsev
    Pages 103-122
  7. Alexey L. Gorodentsev
    Pages 123-154
  8. Alexey L. Gorodentsev
    Pages 155-171
  9. Alexey L. Gorodentsev
    Pages 173-204
  10. Alexey L. Gorodentsev
    Pages 205-228
  11. Alexey L. Gorodentsev
    Pages 229-252
  12. Alexey L. Gorodentsev
    Pages 253-278
  13. Alexey L. Gorodentsev
    Pages 279-307
  14. Alexey L. Gorodentsev
    Pages 309-334
  15. Alexey L. Gorodentsev
    Pages 335-360
  16. Alexey L. Gorodentsev
    Pages 361-386
  17. Alexey L. Gorodentsev
    Pages 387-420
  18. Alexey L. Gorodentsev
    Pages 421-457
  19. Alexey L. Gorodentsev
    Pages 459-479
  20. Alexey L. Gorodentsev
    Pages 481-502
  21. Alexey L. Gorodentsev
    Pages 503-518
  22. Back Matter
    Pages 519-564

About this book

Introduction

This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them.

The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses.

This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.

Keywords

Fields Rings Modules Groups Linear Algebra Multilinear Algebra Representation Theory Commutative Algebra Algebraic Varieties Galois Theory

Authors and affiliations

  • Alexey L. Gorodentsev
    • 1
  1. 1.Faculty of MathematicsNational Research University “Higher School of Economics”MoscowRussia

Bibliographic information