Relative Homological Algebra
eBook - PDF

Relative Homological Algebra

  1. 350 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Relative Homological Algebra

Book details
Table of contents
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Yes, you can access Relative Homological Algebra by Edgar E. Enochs, Overtoun M. G. Jenda in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2011
ISBN
9783110803662
Edition
1
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Preface
  2. 1 Basic Concepts
  3. 1.1 Zornā€™s lemma, ordinal and cardinal numbers
  4. 1.2 Modules
  5. 1.3 Categories and functors
  6. 1.4 Complexes of modules and homology
  7. 1.5 Direct and inverse limits
  8. 1.6 I-adic topology and completions
  9. 2 Flat Modules, Chain Conditions and Prime Ideals
  10. 2.1 Flat modules
  11. 2.2 Localization
  12. 2.3 Chain conditions
  13. 2.4 Prime ideals and primary decomposition
  14. 2.5 Artin-Rees lemma and Zariski rings
  15. 3 Injective and Flat Modules
  16. 3.1 Injective modules
  17. 3.2 Natural identities, flat modules, and injective modules
  18. 3.3 Injective modules over commutative noetherian rings
  19. 3.4 Matlis duality
  20. 4 Torsion Free Covering Modules
  21. 4.1 Existence of torsion free precovers
  22. 4.2 Existence of torsion free covers
  23. 4.3 Examples
  24. 4.4 Direct sums and products
  25. 5 Covers
  26. 5.1 F-precovers and covers
  27. 5.2 Existence of precovers and covers
  28. 5.3 Projective and flat covers
  29. 5.4 Injective covers
  30. 5.5 Direct sums and T-nilpotency
  31. 6 Envelopes
  32. 6.1 F-preenvelopes and envelopes
  33. 6.2 Existence of preenvelopes
  34. 6.3 Existence of envelopes
  35. 6.4 Direct sums of envelopes
  36. 6.5 Flat envelopes
  37. 6.6 Existence of envelopes for injective structures
  38. 6.7 Pure injective envelopes
  39. 7 Covers, Envelopes, and Cotorsion Theories
  40. 7.1 Definitions and basic results
  41. 7.2 Fibrations, cofibrations and Wakamatsu lemmas
  42. 7.3 Set theoretic homological algebra
  43. 7.4 Cotorsion theories with enough injectives and projectives
  44. 8 Relative Homological Algebra and Balance
  45. 8.1 Left and right F-resolutions
  46. 8.2 Derived functors and balance
  47. 8.3 Applications to modules
  48. 8.4 F-dimensions
  49. 8.5 Minimal pure injective resolutions of flat modules
  50. 8.6 Ī» and Ī¼-dimensions
  51. 9 Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules
  52. 9.1 Iwanaga-Gorenstein rings
  53. 9.2 The minimal injective resolution of R
  54. 9.3 More on flat and injective modules
  55. 9.4 Torsion products of injective modules
  56. 9.5 Local cohomology and the dualizing module
  57. 10 Gorenstein Modules
  58. 10.1 Gorenstein injective modules
  59. 10.2 Gorenstein projective modules
  60. 10.3 Gorenstein flat modules
  61. 10.4 Foxby classes
  62. 11 Gorenstein Covers and Envelopes
  63. 11.1 Gorenstein injective precovers and covers
  64. 11.2 Gorenstein injective preenvelopes
  65. 11.3 Gorenstein injective envelopes
  66. 11.4 Gorenstein essential extensions
  67. 11.5 Gorenstein projective precovers and covers
  68. 11.6 Auslanderā€™s last theorem (Gorenstein projective covers)
  69. 11.7 Gorenstein flat covers
  70. 11.8 Gorenstein flat and projective preenvelopes
  71. 12 Balance over Gorenstein and Cohen-Macaulay Rings
  72. 12.1 Balance of Hom(ā€“,ā€“)
  73. 12.2 Balance of ā€“ āŠ— ā€“
  74. 12.3 Dimensions over n-Gorenstein rings
  75. 12.4 Dimensions over Cohen-Macaulay rings
  76. 12.5 Ī©-Gorenstein modules
  77. Bibliographical Notes
  78. Bibliography
  79. Index