Skip to main content
SpringerLink
Log in

A Guide to valuated 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. Bishop, E., Foundations of constructive analysis, McGraw-Hill, 1967.

    Google Scholar 

  2. Brown, R., Valued vector spaces of countable dimension, Publ. Math. Debrecen 18(1971) 149–151.

    MathSciNet  MATH  Google Scholar 

  3. Charles, B., Etude des groups abéliens primaires de type ≤ θ, Ann. Univ. Saraviensis, IV, 3(1955) 184–199.

    MathSciNet  Google Scholar 

  4. _____, Sous-groupes de base des groupes abéliens primaires, Séminaire Dubreil-Pisot, 13e année, 1959/60, no 17.

    Google Scholar 

  5. _____, Sous-groupes fonctoriels et topologies, Studies on abelian groups, Dunod, Paris 1968, 75–92.

    Google Scholar 

  6. Cohen, Joel M., and Herman Gluck, Stacked bases for modules over principal ideal domains, J. Algebra 14(1970) 493–505.

    Article  MathSciNet  MATH  Google Scholar 

  7. Fuchs, L., Infinite abelian groups, Volumes I & II, Academic Press 1970 and 1973.

    Google Scholar 

  8. _____, On pω+n-projective p-groups, Publ. Math. Debrecen (to appear)

    Google Scholar 

  9. _____, Vector spaces with valuations, J. Algebra 35 (1975) 23–38.

    Article  MathSciNet  MATH  Google Scholar 

  10. Fuchs, L., and J. M. Irwin, On pω+1-projective p-groups, Proc. London Math. Soc., 30 (1975) 459–470.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hill, Paul, Certain pure subgroups of primary groups, Topics in abelian groups, Irwin & Walker eds. Scott, Foresman 1963, 311–314.

    Google Scholar 

  12. Hill, P., and C. Megibben, On direct sums of countable groups and generalizations, Studies on abelian groups, Dunod, Paris 1968, 183–206.

    Google Scholar 

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

    Google Scholar 

  14. _____, Finite direct sums of cyclic valuated p-groups, Pac. J. Math. 69 (1977) 97–104.

    Article  MathSciNet  MATH  Google Scholar 

  15. _____, Simply presented valuated p-groups, J. of Algebra (to appear).

    Google Scholar 

  16. Richman, F., Extensions of p-bounded groups, Arch. der Math. 21 (1970) 449–454.

    Article  MathSciNet  MATH  Google Scholar 

  17. _____, The constructive theory of countable abelian p-groups, Pac. J. Math. 45 (1973) 621–637.

    Article  MathSciNet  MATH  Google Scholar 

  18. _____, The constructive theory of KT-modules, Pac. J. Math. 61 (1975) 621–637.

    Article  MathSciNet  MATH  Google Scholar 

  19. _____, Computing heights in Tor, Houston J. Math. (to appear).

    Google Scholar 

  20. Richman, F., and E. A. Walker, Ext in pre-abelian categories, Pac. J. Math. (to appear).

    Google Scholar 

  21. _____, Valuated groups, Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Warfield, R. B. 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 

  25. _____, Classification theory of abelian groups, II: Local theory, (to appear).

    Google Scholar 

Download references

Authors
  1. Fred Richman
    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

Richman, F. (1977). A Guide to valuated 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/BFb0068190

Download citation

  • DOI: https://doi.org/10.1007/BFb0068190

  • 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