Overview
- Provides a gentle, yet thorough, introduction to abstract algebra
- Includes careful proofs of theorems and numerous worked examples
- Written in an informal, readable style
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (14 chapters)
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Front Matter
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Preliminaries
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Front Matter
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Rings
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Front Matter
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Fields and Polynomials
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Front Matter
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Applications
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Front Matter
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Keywords
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.Reviews
“The book provides the reader with valuable technical information regarding the introductory notions and main results of abstract algebra. The author presents concepts, theorems and applications in a very clear and fluent way within the manuscript. Thus, ‘Abstract Algebra. An Introductory Course’ is obviously a well written document with respect to the field of abstract algebra.” (Diana Maimut, zbMATH 1401.00003, 2019)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Abstract Algebra
Book Subtitle: An Introductory Course
Authors: Gregory T. Lee
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-77649-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-77648-4Published: 26 April 2018
eBook ISBN: 978-3-319-77649-1Published: 13 April 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XI, 301
Number of Illustrations: 7 b/w illustrations
Topics: Group Theory and Generalizations, Associative Rings and Algebras, Field Theory and Polynomials