Chapter 30. Large kernels of cellular covers and large localisations

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Introduction xvii
4. List of Symbols xxv
5. Part I. Some useful classes of modules
6. Chapter 1. S-completions 3
7. Chapter 2. Pure-injective modules 22
8. Chapter 3. Mittag-Leffler modules 47
9. Chapter 4. Slender modules 80
10. Part II. Approximations and cotorsion pairs
11. Chapter 5. Approximations of modules 115
12. Chapter 6. Complete cotorsion pairs 131
13. Chapter 7. Hill lemma and its applications 155
14. Chapter 8. Deconstruction of the roots of Ext 196
15. Chapter 9. Modules of projective dimension one 221
16. Chapter 10. Kaplansky classes and abstract elementary classes 228
17. Chapter 11. Independence results for cotorsion pairs 253
18. Chapter 12. The lattice of cotorsion pairs 266
19. Part III. Tilting and cotilting approximations
20. Chapter 13. Tilting approximations 295
21. Chapter 14. 1-tilting modules and their applications 330
22. Chapter 15. Cotilting classes 364
23. Chapter 16. Tilting and cotilting classes over commutative noetherian rings 382
24. Chapter 17. Tilting approximations and the finitistic dimension conjectures 400
25. Bibliography 419
26. Index 451
27. Part IV Prediction principles
28. Chapter 18. Survey of prediction principles using ZFC and more 461
29. Chapter 19. Prediction principles in ZFC: the Black Boxes and others 478
30. Part V. Endomorphism algebras and automorphism groups
31. Chapter 20. Realising algebras – by algebraically independent elements and by prediction principles 531
32. Chapter 21. Automorphism groups of torsion-free abelian groups 578
33. Chapter 22. Modules with distinguished submodules 597
34. Chapter 23. R-modules and fields from modules with distinguished submodules 636
35. Chapter 24 Endomorphism algebras of א_n-free modules 659
36. Part VI. Modules and rings related to algebraic topology
37. Chapter 25. Localisations and cellular covers, the general theory for R-modules 719
38. Chapter 26. Tame and wild localisations of size ≤ 2 ^ℵ₀ 752
39. Chapter 27. Tame cellular covers 773
40. Chapter 28. Wild cellular covers 782
41. Chapter 29. Absolute E-rings 792
42. Part VII. Cellular covers, localisations and E(R)-algebras
43. Chapter 30. Large kernels of cellular covers and large localisations 815
44. Chapter 31. Mixed E(R)-modules over Dedekind domains 832
45. Chapter 32. E(R)-modules with cotorsion 840
46. Chapter 33. Generalised E(R)-algebras 853
47. Chapter 34. Some more useful classes of algebras 913
48. Bibliography 933
49. Index 965