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Abstract Algebra

A First Course, Second Edition

Dan Saracino

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

$54.95 list, 313 pages

10-digit ISBN: 1-57766-536-8

13-digit ISBN: 978-1-57766-536-6

© 2008

Table of Contents

0. Sets and Induction

1. Binary Operations

2. Groups

3. Fundamental Theorems about Groups

4. Powers of an Element; Cyclic Groups

5. Subgroups

6. Direct Products

7. Functions

8. Symmetric Groups

9. Equivalence Relations; Cosets

10. Counting the Elements of a Finite Group

11. Normal Subgroups

12. Homomorphisms

13. Homomorphisms and Normal Subgroups

14. Direct Products and Finite Abelian Groups

15. Sylow Theorems

16. Rings

17. Subrings, Ideals, and Quotient Rings

18. Ring Homomorphisms

19. Polynomials

20. From Polynomials to Fields

21. Unique Factorization Domains

22. Extensions of Fields

23. Constructions with Straightedge and Compass

24. Normal and Separable Extensions

25. Galois Theory

26. Solvability