A comprehensive approach to abstract algebra, in a powerful eText format A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra, and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose. This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Groebner bases. Key to the 8th Edition has been transforming from a print-based learning tool to a digital learning tool. The eText is packed with content and tools, such as mini-lecture videos and interactive figures, that bring course content to life for students in new ways and enhance instruction. A low-cost, loose-leaf version of the text is also available for purchase within the Pearson eText. For courses in Abstract Algebra. Pearson eText is an easy-to-use digital textbook that you can purchase on your own or instructors can assign for their course. The mobile app lets you keep on learning, no matter where your day takes you, even offline. You can also add highlights, bookmarks, and notes in your Pearson eText to study how you like. NOTE: This ISBN is for the Pearson eText access card. Pearson eText is a fully digital delivery of Pearson content. Before purchasing, check that you have the correct ISBN. To register for and use Pearson eText, you may also need a course invite link, which your instructor will provide. Follow the instructions provided on the access card to learn more.
Instructor's Preface Dependence Chart Student's Preface 0. Sets and Relations I. GROUPS AND SUBGROUPS 1. Binary Operations 2. Groups 3. Abelian Groups 4. Nonabelian Examples 5. Subgroups 6. Cyclic Groups 7. Generating Sets and Cayley Digraphs II. STRUCTURE OF GROUPS 8. Groups and Permutations 9. Finitely Generated Abelian Groups 10. Cosets and the Theorem of Lagrange 11. Plane Isometries III. HOMOMORPHISMS AND FACTOR GROUPS 12. Factor Groups 13. Factor-Group Computations and Simple Groups 14. Groups Actions on a Set 15. Applications of G -Sets to Counting IV. ADVANCED GROUP THEORY 16. Isomorphism Theorems 17. Sylow Theorems 18. Series of Groups 19. Free Abelian Groups 20. Free Groups 21. Group Presentations V. RINGS AND FIELDS 22. Rings and Fields 23. Integral Domains 24. Fermat's and Euler's Theorems 25. Encryption VI. CONSTRUCTING RINGS AND FIELDS 26. The Field of Quotients of an Integral Domain 27. Rings and Polynomials 28. Factorization of Polynomials over Fields 29. Algebraic Coding Theory 30. Homomorphisms and Factor Rings 31. Prime and Maximal Ideals 32. Noncommutative Examples VII. COMMUTATIVE ALGEBRA 33. Vector Spaces 34. Unique Factorization Domains 35. Euclidean Domains 36. Number Theory 37. Algebraic Geometry 38. Gr oebner Basis for Ideals VIII. EXTENSION FIELDS 39. Introduction to Extension Fields 40. Algebraic Extensions 41. Geometric Constructions 42. Finite Fields IX. Galois Theory 43. Introduction to Galois Theory 44. Splitting Fields 45. Separable Extensions 46. Galois Theory 47. Illustrations of Galois Theory 48. Cyclotomic Extensions 49. Insolvability of the Quintic