دانلود کتاب Lectures on Artinian Rings

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Preface of the editor
From the preface to the German edition
Chapter I. Sets, relations
1. Sets, relations, mappings
2. Partially ordered and ordered sets
3. The Kuratowski-Zorn Lemma
4. Abstract dependence
Exercises to Chapter I
Hints
References to Chapter I
Chapter II. General properties of rings
5. Rings
6. Ideals, factor rings
7. Rings of power series and rings of polynomials
8. Full matrix rings
9. Embeddings of rings, the Dorroh extension
10. Direct sums of rings
11. Subdirect sums of rings
12. Prime ideals and prime rings
13. Regular rings and their subdirect representations
14. Abelian groups
Exercises to Chapter II
Hints 2.2-2.14
Hints 2.15-2.52
Hints 2.53-2.81
Hints 2.84-2.85
References to Chapter II
Chapter III. Modules and algebras
15. R-modules
16. A module-theoretic characterization of the Dorroh extension
17. Free modules and projective modules
18. Simple modules and completely reducible modules
19. A characterization of completely reducible modules
20. Vector spaces
21. Algebras
Exercises to Chapter III
Hints
References to Chapter III
Chapter IV. The radical
22. Primitive rings and primitive ideals, modular right ideals
23. Examples of primitive rings
24. The radical of a ring
25. Some characterizations of the radical
26. The radicals of related rings
Exercises to Chapter IV
Hints 4.4-4.6
Hints 4.8-4.23
Hints 4.24-4.32
References to Chapter IV
Chapter V. Artinian rings in general
27. Artinian and noetherian modules
28. Artinian and noetherian rings
29. Minimum condition and maximum condition for left ideals
30. Nilpotent right ideals. The radical of an artinian ring
31. Non-nilpotent right ideals. Idempotent elements
32. Further results on idempotents
33. The socle of a module and of a ring
34. The radical of an algebra
Exercises to Chapter V
Hints 5.2-5.12
Hints 5.13-5.24
Hints 5.26-5.29
References to Chapter V
Chapter VI. Rings of linear transformations
35. Vector spaces and rings of matrices
36. Left ideals and automorphisms of a matrix ring over a field
37. A Galois connection for finite dimensional vector spaces
38. The Density Theorem of Jacobson
39. The finite topology of Hom_K (V, V)
40. Some consequences of the Density Theorem
41. The Wedderburn-Artin Theorem
42. The Litoff-Ánh Theorem (by R. Wiegandt)
43. Regularity of linear transformations
Exercises to Chapter VI
Hints 6.2-6.14
References to Chapter VI
Chapter VII. Semi-simple, primary and completely primary rings
44. Quasi-ideals
45. Ideal-theoretic characterization of semi-simple rings
46. Maschke\'s Theorem
47. Indecomposable right ideals and completely primary rings
48. The representation of artinian rings as direct sums of indecomposable right ideals
49. Primary rings
Exercises to Chapter VII
Hints 7.1-7.15
References to Chapter VII
Chapter VIII. Artinian rings as operator domains
50. Semi-simple rings, projective and injective modules
51. Modules over semi-simple rings
52. Systems of equations over modules
53. Injective modules and semi-simple rings
54. Systems of linear equations over semi-simple rings
55. The injective hull (by R. Wiegandt)
56. A characterization of artinian modules (by R. Wiegandt)
Exercises to Chapter VIII
Hints 8.1-8.6
References to Chapter VIII
Chapter IX. The additive groups of artinian rings
57. General remarks on the additive groups of rings
58. The additive groups of artinian rings
59. Artinian rings which are noetherian
60. Noetherian rings which are artinian
61. Artinian rings with identity
62. The splitting of artinian rings
63. Embedding theorems for artinian rings
64. Abelian groups whose full endomorphism rings are artinian
Exercises to Chapter IX
Hints 9.2-9.15
References to Chapter IX
Chapter X. Decomposition of artinian rings (by A. Widiger)
65. Strictly artinian rings
66. The general decomposition theorem
67. Hereditarily artinian rings. Applications
Exercises to Chapter X
Hints 10.3-10.6
References to Chapter X
Chapter XI. Artinian rings of quotients (by G. Betsch)
68. Prerequisites, notations and formulation of the problem
69. The Theorems of Goldie
70. Noetherian orders in artinian rings
Exercises to Chapter XI
References to Chapter XI
Chapter XII. Group rings. A theorem of Connell (by G. Betsch)
71. Group rings
72. Noetherian, regular and semi-simple group rings
73. Artinian group rings
Exercises to Chapter XII
Hints 12.3-12.6
References to Chapter XII
Chapter XIII. Quasi·Frobenius rings (by G. Betsch)
74. Preliminaries
75. The main theorem on QF-rings
76. Modules over QF-rings
Exercises to Chapter XIII
Hints
References to Chapter XIII
Chapter XIV. Rings with minimum condition on principal right ideals (by R. Wiegandt)
77. Simple MHR-rings
78. Semi-primitive and radical MHR-rings
79. Rees matrix rings
80. More on MHR-rings
81. The splitting of MHR-rings
Exercises to Chapter XIV
Hints 14.1-14.4
Hints 14.5-14.7
References to Chapter XIV
Chapter XV. Linearly compact rings (by A. Widiger)
82. Topological modules
83. Linearly compact modules and rings
84. Semi-primitive linearly compact rings
85. Decomposition of strictly linearly compact rings into direct sums of right ideals
86. Linearly compact rings whose radicals are linearly compact groups
Exercises to Chapter XV
Hints
References to Chapter XV
Hints for the solution of the exercises
Bibliography
List of symbols
Author index
Subject index