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Criteria for freeness in groups and valuated vector spaces

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

Keywords

  • Abelian Group
  • Free Space
  • Commutative Ring
  • Countable Group
  • Countable Dimension

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References

  1. G. Bergman, Boolean rings of projection maps, J. London Math. Soc. 4 (1972), 593–598.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. S. Chase, On group extensions and a problem of J. H. C. Whitehead, Topics in Abelian groups, Chicago, Illinois (1963), 173–193.

    Google Scholar 

  3. P. Eklof, Independence results in algebra, Yale lecture notes, 1975.

    Google Scholar 

  4. L. Fuchs, Vector spaces with valuations, J. Algebra 35 (1975), 23–38.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____, Separability of torsion free groups and a problem of J. H. C. Whitehead, Illinois J. Math. 12 (1968), 654–659.

    MathSciNet  MATH  Google Scholar 

  7. _____, Extensions of free groups by torsion groups, Proc. Amer. Math. Soc. 24 (1970), 677–679.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. P. Hill, The additive group of commutative rings generated by idempotents, Proc. Amer. Math. Soc. 38 (1973), 499–502.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. _____, On the freeness of abelian groups: a generalization of Pontryagin’s theorem, Bull. Amer. Math. Soc. 76 (1970), 1118–1120.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. _____, New criteria for freeness in abelian groups, Trans. Amer. Math. Soc. 182 (1973), 201–209.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. _____, New Criteria for freeness in abelian groups, II, Trans. Amer. Math. Soc. 196 (1974), 191–201.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. G. Nöbeling, Verallgemeinerung eines Satzes von Herrn E. Specker, Invent. Math. 6 (1968), 41–55.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  14. L. Pontryagin, The theory of topological commutative groups, Ann. Math. 35 (1934), 361–388.

    CrossRef  MathSciNet  Google Scholar 

  15. F. Richman and E. Walker, Valuated groups, to appear.

    Google Scholar 

  16. J. Rotman, On a problem of Baer and a problem of Whitehead in abelian groups, Acta. Math. Acad. Sci. Hungar. 12 (1961), 245–254.

    CrossRef  MATH  Google Scholar 

  17. S. Shelah, Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243–256.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. E. Specker, Additive Gruppen von Folgen ganzer Zahlen, Portugaliae Math. 9 (1950), 131–140.

    MathSciNet  MATH  Google Scholar 

  19. K. Stein, Analytiche Funktionen mehrerer komplexes Veranderlichen zu vorgegebenen Periodizitatsmoduln und das zweite Cousinsche Problem, Math. Ann. 123 (1951), 201–222.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. D. Thomas, On the freeness of valued vector spaces, preprint.

    Google Scholar 

  21. J. Irwin and E. Walker, Topics in Abelian groups, Chicago, Illinois, 1963.

    Google Scholar 

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© 1977 Springer-Verlag

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Hill, P. (1977). Criteria for freeness in groups and valuated vector spaces. 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/BFb0068193

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  • DOI: https://doi.org/10.1007/BFb0068193

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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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