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Modules over Commutative Regular Rings.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1967Copyright date: ©1967Edition: 1st edDescription: 1 online resource (116 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470400187
Subject(s): Genre/Form: Additional physical formats: Print version:: Modules over Commutative Regular RingsLOC classification:
  • QA251.3.P54 1967
Online resources:
Contents:
Intro -- Contents -- Part I. The Representation Theory -- 1. Subdirect representations of modules -- 2. The decomposition space of a ring -- 3. Sheaves -- 4. Reduced ringed spaces -- 5. The isomorphism theorem -- 6. Functorial properties of ringed spaces -- 7. Functorial properties of sheaves of modules -- 8. The adjoint functor theorem -- 9. Change of ring -- 10. Regular ringed spaces -- 11. Biregular rings -- 12. m-Rings -- Part II. Modules Over Commutative Regular Rings -- 13. The dimension function -- 14. Cyclic modules -- 15. Projective modules -- 16. The Grothendieck group -- 17. Direct sums of cyclic sheaves -- 18. The refinement theorem -- 19. Torsion and torsion-free modules -- 20. Decomposition of torsion free modules -- 21. The decomposition problem -- 22. The torsion subsheaf -- 23. Injective modules -- 24. Self-infective rings -- 25. Questions and conjectures.
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Intro -- Contents -- Part I. The Representation Theory -- 1. Subdirect representations of modules -- 2. The decomposition space of a ring -- 3. Sheaves -- 4. Reduced ringed spaces -- 5. The isomorphism theorem -- 6. Functorial properties of ringed spaces -- 7. Functorial properties of sheaves of modules -- 8. The adjoint functor theorem -- 9. Change of ring -- 10. Regular ringed spaces -- 11. Biregular rings -- 12. m-Rings -- Part II. Modules Over Commutative Regular Rings -- 13. The dimension function -- 14. Cyclic modules -- 15. Projective modules -- 16. The Grothendieck group -- 17. Direct sums of cyclic sheaves -- 18. The refinement theorem -- 19. Torsion and torsion-free modules -- 20. Decomposition of torsion free modules -- 21. The decomposition problem -- 22. The torsion subsheaf -- 23. Injective modules -- 24. Self-infective rings -- 25. Questions and conjectures.

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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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