Abstract Algebra

John W. Lawrence is Professor Emeritus at the University of Waterloo. He was born in Ottawa, Canada, and received degrees from Carleton University and McGill University. After a year of postdoctoral work at the University of Chicago, he joined the Pure Mathematics Department of the University of Waterloo. He now lives with his wife Louise, in Thornhill Canada, where he continues his research in mathematics and probability. Frank A. Zorzitto is Professor Emeritus at the University of Waterloo. After receiving his doctorate at Queen's University in Kingston, Canada, he served for forty years as a researcher in algebra and a professor in the Pure Mathematics Department at the University of Waterloo, and served as Department Chair for twelve years. In recognition of his commitment to the education of students, he received the University's Distinguished Teaching Award. Upon his retirement he was made an Honorary Member of the University. Currently he offers an online course to high school math teachers, based on his e-book A Taste of Number Theory. He continues to teach and to write in his retirement.

'This is a very good book, which provides an excellent introduction to modern algebra for senior undergraduate or beginning graduate students. The book includes a thorough coverage of the standard topics in the theories of groups, rings, fields, modules and Galois theory, taking a conceptual approach to algebra. For instance, the group theory part focuses on group actions, the ring theory exposition very appropriately stresses unique factorization properties, and the Galois theory part details some rather conceptual applications. Some of the less standard, very interesting topics are also present, including the breaking of the Enigma machine, as well as an in-depth look at division algorithms, including Gröbner bases. The book includes numerous exercises. All in all, a great new algebra text!' Lenny Fukshansky, Claremont McKenna College

• Contents; Preface; 1. A refresher on the integers; 2. A first look at groups; 3. Groups acting on sets; 4. Basics on rings-mostly commutative; 5. Primes and unique factorization; 6. Algebraic field extensions; 7. Applications of galois theory; 8. Modules over principal ideal domains; 9. Division algorithms; Appendix A: Infinite sets.