Skip to main content
SpringerLink
Log in

Classification theory of abelian groups, II: Local theory

  • Contributed Papers
  • Conference paper
  • First Online:
Abelian Group Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 874))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Arnold, R. Hunter, and F. Richman, Global Azumaya Theorems in Additive Categories, J. Pure Appl. Alg. 16(1980), 223–242.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Mo Bang, Countably generated modules over complete discrete valuation rings, J. Alg. 14(1970), 552–560.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Mo Bang, Direct sums of countably generated modules over complete discrete valuation rings, Proc. Amer. Math. Soc. 28(1971), 381–388.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Crawley and A. W. Hales, The structure of Abelian p-groups given by certain presentations, J. Alg. 12(1969), 10–23.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. Fuchs, "Infinite Abelian Groups," 2 vols., Academic Press, New York, 1970 and 1973.

    MATH  Google Scholar 

  6. P. Hill, On the classification of Abelian groups, lecture notes.

    Google Scholar 

  7. R. Hunter, Balanced subgroups of Abelian groups, Trans. Amer. Math. Soc. 215 (1976), 81–98.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Hunter and F. Richman, Global Warfield Groups, to appear, Trans. Amer. Math. Soc.

    Google Scholar 

  9. R. Hunter, F. Richman, and E. Walker, Warfield modules, in "Abelian Group Theory" (Proceedings of the 2nd New Mixico State University Conference, 1976), Lecture Notes in Mathematics 616, Springer-Verlag, Berlin, 1977, pp. 87–123.

    Chapter  Google Scholar 

  10. R. Hunter, F. Richman, and E. Walker, Existence theorems for Warfield groups, Trans. Amer. Math. Soc. 235(1978), 345–362.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Hunter and E. Walker, S-groups revisited, (preprint).

    Google Scholar 

  12. I. Kaplansky, "Infinite Abelian Groups," revised edition, Ann Arbor, 1969.

    Google Scholar 

  13. I. Kaplansky and G. W. Mackey, A generalization of Ulm's theorem, Summa Brasil. Math. 2(1951), 195–202.

    MathSciNet  MATH  Google Scholar 

  14. E. Lady, Nearly isomorphic torsion-free Abelian groups, J. Alg. 35(1975), 235–238.

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Megibben, Modules over an incomplete discrete valuation ring, Proc. Amer. Math. Soc. 19(1968), 450–452.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Nunke, Homology and direct sums of countable Abelian groups, Math. Zeit. 101 (1967), 182–212.

    Article  MathSciNet  MATH  Google Scholar 

  17. F. Richman and E. A. Walker, Extending Ulm's theorem without group theory, Proc. Amer. Math. Soc. 21(1969), 194–196.

    MathSciNet  MATH  Google Scholar 

  18. J. Rotman, Mixed modules over valuation rings, Pac. J. Math. 10(1960), 607–623.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Rotman and Ti Yen, Modules over a complete discrete valuation ring, Trans. Amer. Math. Soc. 98(1961), 242–254.

    Article  MathSciNet  MATH  Google Scholar 

  20. R. O. Stanton, An invariant for modules over a discrete valuation ring, Proc. Amer. Math. Soc. 49(1975), 51–54.

    Article  MathSciNet  MATH  Google Scholar 

  21. R. O. Stanton, Decomposition bases and Ulm's theorem, in "Abelian Group Theory" (Proceedings of the 2nd New Mexico State University Conference, 1976) Lecture Notes in Mathematics 616, Springer-Verlag, Berlin, 1977, pp. 39–56.

    Chapter  Google Scholar 

  22. R. O. Stanton, Almost affable Abelian groups, J. Pure Appl. Alg. 15(1979), 41–52.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. O. Stanton, S-groups, preprint.

    Google Scholar 

  24. R. O. Stanton, Warfield groups and S-groups, preprint.

    Google Scholar 

  25. A. E. Stratton, Mixed modules over an incomplete discrete valuation ring, Proc. London Math. Soc. 21(1970), 201–218.

    Article  MathSciNet  MATH  Google Scholar 

  26. C. Walker and R. B. Warfield, Jr., Unique decomposition and isomorphic refinement theorems in additive categories, J. Pure Appl. Alg. 7(1976), 347–359.

    Article  MathSciNet  MATH  Google Scholar 

  27. E. A. Walker, Ulm's theorem for totally projective groups, Proc. Amer. Math. Soc. 37(1973), 387–392.

    MathSciNet  MATH  Google Scholar 

  28. E. A. Walker, The Groups Pβ, Symposia Mathematica XIII, (Gruppi Abeliani), Academic Press, London, 1974, 245–255.

    Google Scholar 

  29. K. Wallace, On mixed groups of torsion-free rank one with totally projective primary components, J. Alg. 17(1971), 482–488.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. B. Warfield, Jr., Classification theorems for p-groups and modules over a discrete valuation ring, Bull. Amer. Math. Soc. 78(1972), 88–92.

    Article  MathSciNet  MATH  Google Scholar 

  31. R. B. Warfield, Jr., Invariants and a classification thoerem for modules over a discrete valuation ring, University of Washington notes, 1971.

    Google Scholar 

  32. R. B. Warfield, Jr., Simply Presented Groups, in Proceedings of the Special Semester on Abelian Groups, Spring 1972, University of Arizona, Tucson.

    Google Scholar 

  33. R. B. Warfield, Jr., A classification theorem for Abelian p-groups, Trans. Amer. Math. Soc. 210(1975), 149–168.

    MathSciNet  MATH  Google Scholar 

  34. R. B. Warfield, Jr., Classification theory of Abelian groups I: Balanced projectives, Trans. Amer. Math. Soc., 222(1976), 33–63.

    MathSciNet  MATH  Google Scholar 

  35. R. B. Warfield, Jr., The structure of mixed Abelian groups, in "Abelian Group Theory" (Proceedings of the 2nd New Mexico State University Conference, 1976) Lecture Notes in Mathematics 616, Springer-Verlag, Berlin, 1977, pp. 1–38.

    Chapter  Google Scholar 

  36. B. D. Wick, A projective characterization for SKT-modules, Proc. Amer. Math. Soc. 80(1980), 39–43.

    Article  MathSciNet  MATH  Google Scholar 

  37. B. D. Wick, A classification theorem for SKT-modules, Proc. Amer. Math. Soc. 80(1980), 44–46.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Robert B. Warfield Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rüdiger Göbel Elbert Walker

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Warfield, R.B. (1981). Classification theory of abelian groups, II: Local theory. In: Göbel, R., Walker, E. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090545

Download citation

  • DOI: https://doi.org/10.1007/BFb0090545

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10855-9

  • Online ISBN: 978-3-540-38767-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation