Approximations and Endomorphism Algebras of Modules : : Volume 1 – Approximations / Volume 2 – Predictions /

Approximations and Endomorphism Algebras of Modules : : Volume 1 – Approximations / Volume 2 – Predictions / / Rüdiger Göbel, Jan Trlifaj.

This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
VerfasserIn:
Göbel, Rüdiger,
Trlifaj, Jan,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2012]
©2012
Year of Publication:2012
Edition:2nd rev. and exp. ed.
Language:English
Series:De Gruyter Expositions in Mathematics , 41
Online Access:
Physical Description:1 online resource (972 p.)
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Table of Contents:
  • Frontmatter
  • Contents
  • Introduction
  • List of Symbols
  • Part I. Some useful classes of modules
  • Chapter 1. S-completions
  • Chapter 2. Pure-injective modules
  • Chapter 3. Mittag-Leffler modules
  • Chapter 4. Slender modules
  • Part II. Approximations and cotorsion pairs
  • Chapter 5. Approximations of modules
  • Chapter 6. Complete cotorsion pairs
  • Chapter 7. Hill lemma and its applications
  • Chapter 8. Deconstruction of the roots of Ext
  • Chapter 9. Modules of projective dimension one
  • Chapter 10. Kaplansky classes and abstract elementary classes
  • Chapter 11. Independence results for cotorsion pairs
  • Chapter 12. The lattice of cotorsion pairs
  • Part III. Tilting and cotilting approximations
  • Chapter 13. Tilting approximations
  • Chapter 14. 1-tilting modules and their applications
  • Chapter 15. Cotilting classes
  • Chapter 16. Tilting and cotilting classes over commutative noetherian rings
  • Chapter 17. Tilting approximations and the finitistic dimension conjectures
  • Bibliography
  • Index
  • Part IV Prediction principles
  • Chapter 18. Survey of prediction principles using ZFC and more
  • Chapter 19. Prediction principles in ZFC: the Black Boxes and others
  • Part V. Endomorphism algebras and automorphism groups
  • Chapter 20. Realising algebras – by algebraically independent elements and by prediction principles
  • Chapter 21. Automorphism groups of torsion-free abelian groups
  • Chapter 22. Modules with distinguished submodules
  • Chapter 23. R-modules and fields from modules with distinguished submodules
  • Chapter 24 Endomorphism algebras of אn-free modules
  • Part VI. Modules and rings related to algebraic topology
  • Chapter 25. Localisations and cellular covers, the general theory for R-modules
  • Chapter 26. Tame and wild localisations of size ≤ 2 ℵ0
  • Chapter 27. Tame cellular covers
  • Chapter 28. Wild cellular covers
  • Chapter 29. Absolute E-rings
  • Part VII. Cellular covers, localisations and E(R)-algebras
  • Chapter 30. Large kernels of cellular covers and large localisations
  • Chapter 31. Mixed E(R)-modules over Dedekind domains
  • Chapter 32. E(R)-modules with cotorsion
  • Chapter 33. Generalised E(R)-algebras
  • Chapter 34. Some more useful classes of algebras
  • Bibliography
  • Index

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