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Algebra. Volume 1.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Pergamon Press,
1967.
|
| Colección: | International series in pure and applied mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Algebra; Copyright Page; Table of Contents; PREFACE TO THE GERMAN EDITION; PREFACE TO THE ENGLISH EDITION; LIST OF SYMBOLS; CHAPTER I. SET-THEORETICAL PRELIMINARIES; 1. Sets; 2. Relations; 3. Mappings; 4. Multiplication of Mappings; 5. Functions; 6. Classification of a Set. Equivalence Relations; 7. Natural Numbers; 8. Equipotent Sets; 9. Ordered and Semiordered Sets; 10. Well-ordered Sets; 11*. The Lemma of Kuratowski-Zorn; 12. The Special Lemma of Kuratowski-Zorn; 13. The Lemma of Teichmiiller-Tukey; 14. The Theorem of Hausdorff-Birkhoff.
- 15. Theorem of Well-ordering 16. Transfinite Induction; CHAPTER II. STRUCTURES; 17. Compositions; 18. Operators; 19. Structures; 20. Semigroups; 21. Groups; 22. Modules; 23. Rings; 24. Skew Fields; 25. Substructures; 26. Generating Elements; 27. Some Important Substructures; 28. Isomorphisms; 29. Homomorphisms; 30. Factor Structures; 31. The Homomorphy Theorem; 32. Automorphisms. Endomorphisms. Autohomomorphisms. Meromorphisms; 33. Isomorphic Structures with the Same Elements; 34. Skew Products; 35. Structure Extensions.
- 36. Representation of Groups by Permutation Groups 37. Endomorphism Rings; 38. Representation of Rings by Endomorphism Rings; 39. Anti-isomorphisms. Anti-automorphisms; 40. Complexes; 41. Cosets. Residue Classes; 42. Normal Divisors. Ideals; 43. Alternating Groups; 44. Direct Products. Direct Sums; 45. Basis; 46. Congruences; 47. Quotient Structures; 48. Difference Structures; 49. Free Structures. Structures Defined by Equations; 50. Schreier Group Extensions; 51. The Holomorph of a Group; 52. Everett Ring Extensions; 53. Double Homothetisms.
- 54. The Holomorphs of a Ring 55. The Two Isomorphy Theorems; 56. Simple Factor Structures; 57. Commutative Factor Structures; 58, Zassenhaus's Lemma; 59. Schreier's Main Theorem and the Jordan-H�older Theorem; 60. Lattices; CHAPTER III. OPERATOR STRUCTURES; 61. Operator Structures; 62. Operator Groups, Operator Modules and Operator Rings; 63. Remak-Krull-Schmidt Theorem; 64. Vector Spaces. Double Vector Spaces. Algebras. Double Algebras; 65. Cross Products; 66. Monomial Rings; 67. Polynomial Rings; 68. Linear Mappings; 69. Full Matrix Rings; 70. Linear Groups.
- 71. Alternating Rings 72. Determinants; 73. Cramer's Rule; 74. Characteristic Polynomials; 75. Norms and Traces; 77. The Quaternion Group; 78. Quaternion Rings; CHAPTER IV. DIVISIBILITY IN RINGS; 79. Factor Decompositions and Divisibility; 80. Ideals and Divisibility; 81. Principal Ideal Rings; 82. Euclidean Rings; 83. Euclid's Algorithm; 84. The Ring of the Integers; 85. Szendrei's Theorem; 86. Polynomial Rings over Skew Fields; 87. The Residue Theorem for Polynomials; 88. Gauss's Theorem; 89.* The Ring of Integral Quaternions.