Abstract Algebra: An Introductory Course

Gregory T. Lee

Apr 2018 · Springer

About this ebook

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.

Ratings and reviews

Excellent text with clear proofs and a nice survey of key topics in abstract algebra. For those using the text for self-study (n.b., I was an undergraduate math major almost 20 years ago, and we used Artin then; I was just revisiting the subject for fun), I found most of the exercises doable -- the hardest ones are usually the even-numbered ones, which don't have solutions. A few had me really stumped, and I had to resort to e-mailing the author for hints, or scouring the internet for solutions. I think those exercises which require some measure of creativity or ingenuity ought to have some hints, or be demarcated with an asterisk.

About the author

Gregory T. Lee is a professor at Lakehead University specializing in group rings, a branch of abstract algebra. He has published numerous papers on the subject, as well as a monograph with Springer.