Format:
Online Ressource (xi, 290 pages)
Edition:
Online-Ausg.
ISBN:
0122696018
Series Statement:
Pure and applied mathematics v. 36, pt. 1
Content:
Preliminaries -- Direct sums -- Direct sums of cyclic groups -- Divisible groups -- Pure subgroups -- Basic subgroups -- Algebraically compact groups -- Homomorphism groups -- Groups of extensions -- X tensor and torsion products
Note:
Includes bibliographical references and indexes. - Print version record
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Front Cover; Infinite Abelian Groups; Copyright Page; Contents; Preface; Chapter I. Preliminaries; 1. Definitions; 2. Maps and Diagrams; 3. The Most Important Types of Groups; 4. Modules; 5. Categories of Abelian Groups; 6. Functorial Subgroups and Quotient Groups; 7. Topologies in Groups; Notes; Chapter II. Direct Sums; 8. Direct Sums and Direct Products; 9. Direct Summands; 10. Pullback and Pushout Diagrams; 11. Direct Limits; 12. Inverse Limits; 13. Completeness and Completions; Notes; Chapter III. Direct Sums of Cyclic Groups; 14. Free Abelian Groups-Defining Relations
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15. Finitely Generated Groups16. Linear Independence and Rank; 17. Direct Sums of Cyclic p-Groups; 18. Subgroups of Direct Sums of Cyclic Groups; 19. Countable Free Groups; Notes; Chapter IV. Divisible Groups; 20. Divisibility; 21. Injective Groups; 22. Systems of Equations; 23. The Structure of Divisible Groups; 24. The Divisible Hull; 25. Finitely Cogenerated Groups; Notes; Chapter V. Pure Subgroups; 26. Purity; 27. Bounded Pure Subgroups; 28. Quotient Groups Modulo Pure Subgroups; 29. Pure-Exact Sequences; 30. Pure-Projectivity and Pure-Injectivity; 31. Generalizations of Purity; Notes
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Chapter VI. Basic Subgroups32. p-Basic Subgroups; 33. Basic Subgroups of p-Groups; 34. Further Results on p-Basic Subgroups; 35. Different p-Basic Subgroups; 36. Basic Subgroups Are Endomorphic Images; 37. The Ulm Sequence; Notes; Chapter VII. Algebraically Compact Groups; 38. Algebraic Compactness; 39. Complete Groups; 40. The Structure of Algebraically Compact Groups; 41. Pure-Essential Extensions; 42. More about Algebraically Compact Groups; Notes; Chapter VIII. Homomorphism Groups; 43. Groups of Homomorphisms; 44. Exact Sequences for Hom; 45. Certain Subgroups of Hom
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46. Homomorphism Groups of Torsion Groups47. Character Groups; 48. Duality between Discrete Torsion and 0-Dimensional Compact Groups; Notes; Chapter IX. Groups of Extensions; 49. Group Extensions; 50. Extensions as Short Exact Sequences; 51. Exact Sequences for Ext; 52. Elementary Properties of Ext; 53. The Functor Pext; 54. Cotorsion Groups; 55. The Structure of Cotorsion Groups; 56. The Ulm Factors of Cotorsion Groups; 57. Applications to Ext; 58. Injective Properties of Cotorsion Groups; Notes; Chapter X. Tensor and Torsion Products; 59. The Tensor Product
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60. Exact Sequences for Tensor Products61. The Structure of Tensor Products; 62. The Torsion Product; 63. Exact Sequences for Tor; 64. The Structure of Torsion Products; Notes; Bibliography; Table of Notations; Author Index; Subject Index; Pure and Applied Mathematics;
Additional Edition:
ISBN 0122696018
Additional Edition:
Erscheint auch als Druck-Ausgabe Infinite Abelian groups. Volume 1 New York, NY : Academic Press, 1970
Language:
English
Keywords:
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