◎作者簡(jiǎn)介 約翰·弗雷利（John B. Fraleigh）是美國(guó)羅德島大學(xué)數(shù)學(xué)與應(yīng)用數(shù)學(xué)科學(xué)系的榮休教授，一生致力于數(shù)學(xué)教育，獲得了諸多贊譽(yù)，羅德島大學(xué)還設(shè)立了以他名字命名的獎(jiǎng)學(xué)金。他出版過(guò)多部有影響力的數(shù)學(xué)教材，《抽象代數(shù)基礎(chǔ)教程》是其代表作之一，多年來(lái)一直被奉為經(jīng)典，長(zhǎng)銷不衰。
圖書目錄
◎圖書目錄 Preface 0. Sets and Relations I. GROUPS AND SUBGROUPS 1. Introduction and Examples 2. Binary Operations 3. Isomorphic Binary Structures 4. Groups 5. Subgroups 6. Cyclic Groups 7. Generators and Cayley Digraphs II. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS 8. Groups of Permutations 9. Orbits, Cycles, and the Alternating Groups 10. Cosets and the Theorem of Lagrange 11. Direct Products and Finitely Generated Abelian Groups 12. Plane Isometries III. HOMOMORPHISMS AND FACTOR GROUPS 13. Homomorphisms 14. Factor Groups 15. Factor-Group Computations and Simple Groups 16. Group Action on a Set 17. Applications of G-Sets to Counting IV. RINGS AND FIELDS 18. Rings and Fields 19. Integral Domains 20. Fermat's and Euler's Theorems 21. The Field of Quotients of an Integral Domain 22. Rings of Polynomials 23. Factorization of Polynomials over a Field 24. Noncommutative Examples 25. Ordered Rings and Fields V. IDEALS AND FACTOR RINGS 26. Homomorphisms and Factor Rings 27. Prime and Maximal Ideas 28. Groebner Bases for Ideals VI. EXTENSION FIELDS 29. Introduction to Extension Fields 30. Vector Spaces 31. Algebraic Extensions 32. Geometric Constructions 33. Finite Fields VII. ADVANCED GROUP THEORY 34. Isomorphism Theorems 35. Series of Groups 36. Sylow Theorems 37. Applications of the Sylow Theory 38. Free Abelian Groups 39. Free Groups 40. Group Presentations VIII. AUTOMORPHISMS AND GALOIS THEORY 41. Automorphisms of Fields 42. The Isomorphism Extension Theorem 43. Splitting Fields 44. Separable Extensions 45. Totally Inseparable Extensions 46. Galois Theory 47. Illustrations of Galois Theory 48. Cyclotomic Extensions 49. Insolvability of the Quintic Appendix: Matrix Algebra Bibliography Notations Index
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