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Decomposition bases and Ulm’s theorem

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Abelian Group Theory

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

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References

  1. R. Baer, Abelian groups without elements of finite order, Duke Math. J. 3(1937), 68–122.

    Article  MathSciNet  MATH  Google Scholar 

  2. 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 

  3. L. Fuchs, Infinite Abelian Groups, Two volumes, Academic Press, New York, 1970, 1973.

    Google Scholar 

  4. P. Griffith, Infinite Abelian Group Theory, University of Chicago Press, Chicago, 1970.

    MATH  Google Scholar 

  5. P. Hill, On the classification of Abelian groups, preprint.

    Google Scholar 

  6. R.H. Hunter, Balanced Subgroups of Abelian Groups, Doctoral dissertation, Australian National University, Canberra, 1975.

    MATH  Google Scholar 

  7. I. Kaplansky, Projective modules, Ann. Math. 68(1958), 372–377.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. G. Kolettis, Direct sums of countable groups, Duke Math. J. 27(1960), 111–125.

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Ya. Kulikov, On direct decompositions of groups, (Russian), Ukrain. Mat. Z. 4(1952), 230–275, 347–372.

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. L.D. Parker and E.A. Walker, An extension of the Ulm-Kolettis theorems, Studies on Abelian Groups, Paris, 1968, 309–325.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. 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 

  19. H. Ulm, Zur Theorie der abzählbar-unendlichen abelschen Gruppen, Math. Ann., 107(1933), 774–803.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  21. K.D. 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 

  22. R.B. Warfield, Jr., Simply presented groups, Proceeding of the Special Semester on Abelian Groups, Spring 1972, University of Arizona, Tucson.

    Google Scholar 

  23. R. B. Warfield, Jr., Classification theory of Abelian groups I, Balanced projectives, to appear.

    Google Scholar 

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

    Google Scholar 

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Authors
  1. Robert O. Stanton
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Editor information

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

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© 1977 Springer-Verlag

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Stanton, R.O. (1977). Decomposition bases and Ulm’s theorem. 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/BFb0068188

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  • DOI: https://doi.org/10.1007/BFb0068188

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08447-1

  • Online ISBN: 978-3-540-37069-7

  • eBook Packages: Springer Book Archive

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