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Representation Type of Commutative Noetherian Rings III : Global Wildness and Tameness.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2005Copyright date: ©2005Edition: 1st edDescription: 1 online resource (187 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470404338
Subject(s): Genre/Form: Additional physical formats: Print version:: Representation Type of Commutative Noetherian Rings IIIDDC classification:
  • 510 s;512/.4
LOC classification:
  • QA251.3 -- .K55 2005eb
Online resources:
Contents:
Intro -- Contents -- 1. Abstract -- 2. Introduction -- Chapter 0. Preliminaries -- 3. Standard Notation and Terminology -- 4. Q-Localization and Minimal Primes -- 5. Ideal-adic Completions -- 6. Primary Components (terminology from abelian groups) -- 7. Elimination of finite-length summands -- 8. Basic Finiteness Conditions -- 9. General Cancellation and Direct Summands in Dimension 1 -- Chapter 1. Dedekind-like Rings -- 10. Definition and Characterizations -- 11. Maximal Ideals: Residue Inclusions, Localizations, Completions -- 12. Surjective Pullback Squares -- 13. Homomorphic Images: Local versus Complete Local -- Chapter 2. Wildness -- 14. Global Dichotomy, Global Wildness -- Chapter 3. Structure of a Genus -- 15. Consistent (Torsionfree) Ranks -- 16. Indecomposable A-modules -- Connections Graph -- Chapter 4. Substitute for Conductor Squares -- 17. Residue Inclusions of Separated Modules -- 18. Separated Covers -- Chapter 5. Isomorphism Classes in a Genus, Idele Group Action -- 19. Restricted Genus and Separated Covers -- 20. Wiegand Lifting Theorem -- 21. Residue Endo-idèles on T-modules -- 22. Residue Unit Idèles -- 23. Stabilizers: Basic properties -- 24. Equality Stabilizers -- Chapter 6. Web of Class Groups -- 25. Genus Class Group, ξ…map, Mayer…Vietoris Sequence -- 26. Cancellation, Restricted Genus, and Idèles -- 27. Super Mayer-Vietoris and faithful modules -- 28. Super Mayer-Vietoris and unfaithful modules -- Chapter 7. Direct Sums -- 29. General Results -- 30. Decomposition of G(M) -- relation to direct summands of M -- 31. Examples: Simplest G(∧) -- Direct…Sum Decompositions -- Chapter 8. Finite Normalization -- 32. [sub(∧)]T versus [sub(T)]T -- 33. Structure of ∧. Another simple G(∧) -- 34. Example: [sub(s)]G = G(M) ≠ G(A) -- 35. Power Isomorphism, Cancellation, Power Cancellation -- 36. Unsplit Mayer…Vietoris.
Example: G(∧) ≠ rG(&amp -- #8743) -- ≠ 0 -- Cancellation in Z|∞| -- Appendix A -- 37. Open Problems -- Appendix B -- 38. Terminology Index -- 39. Notation Index -- Bibliography.
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Intro -- Contents -- 1. Abstract -- 2. Introduction -- Chapter 0. Preliminaries -- 3. Standard Notation and Terminology -- 4. Q-Localization and Minimal Primes -- 5. Ideal-adic Completions -- 6. Primary Components (terminology from abelian groups) -- 7. Elimination of finite-length summands -- 8. Basic Finiteness Conditions -- 9. General Cancellation and Direct Summands in Dimension 1 -- Chapter 1. Dedekind-like Rings -- 10. Definition and Characterizations -- 11. Maximal Ideals: Residue Inclusions, Localizations, Completions -- 12. Surjective Pullback Squares -- 13. Homomorphic Images: Local versus Complete Local -- Chapter 2. Wildness -- 14. Global Dichotomy, Global Wildness -- Chapter 3. Structure of a Genus -- 15. Consistent (Torsionfree) Ranks -- 16. Indecomposable A-modules -- Connections Graph -- Chapter 4. Substitute for Conductor Squares -- 17. Residue Inclusions of Separated Modules -- 18. Separated Covers -- Chapter 5. Isomorphism Classes in a Genus, Idele Group Action -- 19. Restricted Genus and Separated Covers -- 20. Wiegand Lifting Theorem -- 21. Residue Endo-idèles on T-modules -- 22. Residue Unit Idèles -- 23. Stabilizers: Basic properties -- 24. Equality Stabilizers -- Chapter 6. Web of Class Groups -- 25. Genus Class Group, ξ…map, Mayer…Vietoris Sequence -- 26. Cancellation, Restricted Genus, and Idèles -- 27. Super Mayer-Vietoris and faithful modules -- 28. Super Mayer-Vietoris and unfaithful modules -- Chapter 7. Direct Sums -- 29. General Results -- 30. Decomposition of G(M) -- relation to direct summands of M -- 31. Examples: Simplest G(∧) -- Direct…Sum Decompositions -- Chapter 8. Finite Normalization -- 32. [sub(∧)]T versus [sub(T)]T -- 33. Structure of ∧. Another simple G(∧) -- 34. Example: [sub(s)]G = G(M) ≠ G(A) -- 35. Power Isomorphism, Cancellation, Power Cancellation -- 36. Unsplit Mayer…Vietoris.

Example: G(∧) ≠ rG(&amp -- #8743) -- ≠ 0 -- Cancellation in Z|∞| -- Appendix A -- 37. Open Problems -- Appendix B -- 38. Terminology Index -- 39. Notation Index -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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