Table of contents

  1. Front Matter
    Pages i-xi
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Gregory T. Lee
      Pages 3-13
    3. Gregory T. Lee
      Pages 15-31
  3. Groups

    1. Front Matter
      Pages 33-33
    2. Gregory T. Lee
      Pages 35-60
    3. Gregory T. Lee
      Pages 61-84
    4. Gregory T. Lee
      Pages 101-113
    5. Gregory T. Lee
      Pages 115-132
  4. Rings

    1. Front Matter
      Pages 133-133
    2. Gregory T. Lee
      Pages 135-148
    3. Gregory T. Lee
      Pages 149-170
    4. Gregory T. Lee
      Pages 171-188
  5. Fields and Polynomials

    1. Front Matter
      Pages 189-189
    2. Gregory T. Lee
      Pages 191-205
    3. Gregory T. Lee
      Pages 207-229
  6. Applications

    1. Front Matter
      Pages 231-231
    2. Gregory T. Lee
      Pages 233-239
    3. Gregory T. Lee
      Pages 241-252
  7. Back Matter
    Pages 253-301

About this book


This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. 

The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions.

Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.


abstract algebra algebra groups rings fields construction of finite fields polynomials MSC (2010) 20-01, 16-01, 12-01

Authors and affiliations

  • Gregory T. Lee
    • 1
  1. 1.Department of Mathematical SciencesLakehead UniversityThunder BayCanada

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77648-4
  • Online ISBN 978-3-319-77649-1
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site