Skip to main content
SpringerLink
Log in

The structure of mixed abelian groups

  • Conference paper
  • First Online:
Abelian Group Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 616))

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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, Genera and decompositions of torsion-free modules, to appear in these proceedings.

    Google Scholar 

  2. D. Arnold and E. Lady, Endomorphism rings and direct sums of torsion-free Abelian groups, Trans. Amer. Math. Soc. 211 (1975), 225–237.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Baer, The subgroup of the elements of finite order in an Abelian group, Ann. Math. 37 (1936), 766–781.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), 69–122.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. H. Bass, K-theory and stable algebra, Pub. Math. I.H.E.S. no. 22 (1964), 5–60.

    Google Scholar 

  8. B. Charles, Sous-groupes fonctoriels et topologies, Studies on Abelian Groups (Sympos., Montpellier, 1967) Springer-Verlag, Berlin and Dunod, Paris, 1968, pp. 75–92.

    Google Scholar 

  9. A.L.S. Corner, On endomorphism rings of primary Abelian p-groups, II, Quart. J. Math. Ox. 27 (1976), 5–13.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Crawley, The cancellation of torsion abelian groups in direct sums, J. Alg. 2 (1965), 432–442.

    Article  MathSciNet  MATH  Google Scholar 

  11. 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 

  12. E. G. Evans, Jr., Krull-Schmidt and cancellation over local rings, Pacific J. Math., 46 (1973), 115–121.

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Fuchs, Notes on Abelian groups, II, Acta Math. Acad. Sci. Hungar. 11 (1960), 117–125.

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Fuchs, On a substitution property for modules, Monatshefte fur Math., 75 (1971), 198–204.

    Article  MathSciNet  MATH  Google Scholar 

  15. L. Fuchs, Infinite Abelian Groups. vol. II, Academic Press, New York, 1973.

    MATH  Google Scholar 

  16. K. R. Goodearl, Power cancellation of groups and modules, Pacific J. Math. 64 (1976), 387–411.

    Article  MathSciNet  MATH  Google Scholar 

  17. P. Griffith, A solution to the splitting mixed group problem of Baer, Trans. Amer. Math. Soc., 139 (1969), 261–269.

    Article  MathSciNet  MATH  Google Scholar 

  18. D. K. Harrison, Infinite Abelian groups and homological methods, Ann. Math. 69 (1959), 366–391; Correction, ibid. 71 (1960), 197.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. K. Harrison, On the structure of Ext, Topics in Abelian Groups, (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman, Chicago, 1963, pp. 195–210.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. R. Hunter, F. Richman, and E. A. Walker, Existence theorems for Warfield groups, Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  22. I. Kaplansky, Maximal fields with valuation, Duke Math. J. 9 (1942), 303–321.

    Article  MathSciNet  MATH  Google Scholar 

  23. I. Kaplansky, Infinite Abelian Groups, U. Mich. Press, Ann Arbor, 1954; rev. ed. 1969.

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  25. G. Kolettis, Homogeneously decomposable modules, Studies on Abelian Groups (Sympos. Montpellier, 1967) Springer-Verlag, Berlin, and Dunod, Paris, 1968, pp. 223–238.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Megibben, On mixed groups of torsion-free rank one, Ill, J. Math. 11 (1967), 134–144.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. R. J. Nunke, Modules of extensions over Dedekind rings, Ill. J. Math. 3 (1959), 222–241.

    MathSciNet  MATH  Google Scholar 

  30. R. J. Nunke, Homology and direct sums of countable Abelian groups, Math. Zeits. 191 (1967), 182–212.

    Article  MathSciNet  MATH  Google Scholar 

  31. R. J. Nunke, Uniquely elongating modules, Proc. Conf. on Abelian Groups, (November, 1972), Symposia Mathematica 13, Academic Press, London, 1974, pp. 315–330.

    MATH  Google Scholar 

  32. F. Richman, The constructive theory of KT-modules, Pacific J. Math. 61 (1975), 263–274.

    Article  MathSciNet  MATH  Google Scholar 

  33. R. Richman and E. A. Walker, Valuated Groups, to appear.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  35. J. Rotman, Torsion-free and mixed Abelian groups, Ill. J. Math. 5 (1961), 131–143.

    MathSciNet  MATH  Google Scholar 

  36. 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 

  37. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  39. A. E. Stratton, A splitting theorem for mixed Abelian groups, Proc. Conf. on Abelian Groups (November, 1972), Symposia Mathematica 13, Acadmemic Press, London, 1974, pp. 109–125.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  42. 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 

  43. R. B. Warfield, Jr., Homomorphisms and duality for torsion-free groups, Math. Zeits. 107 (1968), 189–200.

    Article  MathSciNet  MATH  Google Scholar 

  44. R. B. Warfield, Jr., An isomorphic refinement theorem for Abelian groups, Pacific J. Math., 34 (1970), 237–255.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  46. 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 

  47. R. B. Warfield, Jr., Simply presented groups, Proc. Sem. Abelian group theory, Univ. of Arizona lecture notes, 1972.

    Google Scholar 

  48. R. B. Warfield, Jr., The uniqueness of elongations of Abelian groups, Pacific J. Math. 52 (1974), 289–304.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  51. R. B. Warfield, Jr., Classification theory of Abelian groups II: Local theory, to appear.

    Google Scholar 

  52. R. B. Warfield, Jr., Cancellation for modules and the stable range of endomorphism rings, to appear.

    Google Scholar 

  53. B. Wick, Classification theorems for infinite Abelian groups, Dissertation, Univ. of Washington, 1972.

    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

David M. Arnold Roger H. Hunter Elbert A. Walker

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Warfield, R.B. (1977). The structure of mixed abelian groups. In: Arnold, D.M., Hunter, R.H., Walker, E.A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068187

Download citation

  • DOI: https://doi.org/10.1007/BFb0068187

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08447-1

  • Online ISBN: 978-3-540-37069-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation