Abstract Algebra: An Introductory Course (Springer Undergraduate Mathematics) (Paperback)

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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.

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.
Product Details
ISBN: 9783319776484
ISBN-10: 3319776487
Publisher: Springer
Publication Date: April 26th, 2018
Pages: 301
Language: English
Series: Springer Undergraduate Mathematics