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A Guide to valuated groups

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

Keywords

  • Height Function
  • Valuate Tree
  • Discrete Valuation Ring
  • Indecomposable Object
  • Pure Subgroup

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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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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© 1977 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08447-1

  • Online ISBN: 978-3-540-37069-7

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