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Algebra II

Textbook for Students of Mathematics

  • Alexey L. Gorodentsev

Table of contents

  1. Front Matter
    Pages i-xv
  2. Alexey L. Gorodentsev
    Pages 1-19
  3. Alexey L. Gorodentsev
    Pages 21-56
  4. Alexey L. Gorodentsev
    Pages 57-73
  5. Alexey L. Gorodentsev
    Pages 75-98
  6. Alexey L. Gorodentsev
    Pages 99-129
  7. Alexey L. Gorodentsev
    Pages 131-150
  8. Alexey L. Gorodentsev
    Pages 151-171
  9. Alexey L. Gorodentsev
    Pages 173-186
  10. Alexey L. Gorodentsev
    Pages 187-226
  11. Alexey L. Gorodentsev
    Pages 227-240
  12. Alexey L. Gorodentsev
    Pages 241-263
  13. Alexey L. Gorodentsev
    Pages 265-293
  14. Alexey L. Gorodentsev
    Pages 295-314
  15. Alexey L. Gorodentsev
    Pages 315-334
  16. Back Matter
    Pages 335-370

About this book

Introduction

This book is the second 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

Authors and affiliations

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

Bibliographic information