Abstract algebra /
Dan Saracino.
- Second, Global edition.
- 313 pages ; 23 cm.
Includes index.
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 Groups 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. Extension of Fields 23. Constructions with Straightedge and Compass 24. Normal and Separable Extensions 25. Galois Theory 26. Solvability
The presentation of the sections is given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and proof of the Primitive Element of Theorem.
College of Education Bachelor of Secondary Education major in Mathematics