Five theorems on abelian groups

  • Irving Kaplansky
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 697)


Abelian Group Projective Group Continuum Hypothesis Principal Ideal Domain Whitehead Group 
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  1. [127]
    D. Arnold, R. Hunter, and E. Walker [Eds.], Abelian Group Theory (Proc. 2nd New Mexico State University Conference, Las Cruces, New Mexico, 1976. Lecture Notes in Mathematics, 616. Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar
  2. [128]
    Gilber Baumslag [Ed.], Reviews on Infinite Groups, 2 (Amer. Math. Soc., Providence, Rhode Island, 1974). (Section XVIII, pages 616–736 is devoted to abelian groups. MR reviews from 1940 through 1970, vols. 1–40 are included.)Google Scholar
  3. [129]
    George M. Bergman, "Boolean rings of projection maps", J. London Math. Soc. (2) 4 (1972), 593–598.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [130]
    Joel M. Cohen and Herman Gluck, "Stacked bases for modules over principal ideal domains", J. Algebra 14 (1970), 493–505.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [131]
    Richard M. Dudley, "Unsolvable problems in mathematics" (Letter to the Editor), Science 191 (1976), 807–808.CrossRefGoogle Scholar
  6. [132]
    Paul C. Eklof, "Whitehead's problem is undecidable", Amer. Math. Monthly 83 (1976), 775–788.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [133]
    László Fuchs, Infinite Abelian Groups, I (Pure and Applied Mathematics, 36. Academic Press, New York, London, 1970).zbMATHGoogle Scholar
  8. [134]
    László Fuchs, Infinite Abelian Groups, II (Pure and Applied Mathematics, 36-II. Academic Press, New York, London, 1973).zbMATHGoogle Scholar
  9. [135]
    Phillip A. Griffith, Infinite Abelian Group Theory (University of Chicago Press, Chicago, Illinois, London; 1970).zbMATHGoogle Scholar
  10. [136]
    Paul Hill, "The additive group of commutative rings generated by idempotents", Proc. Amer. Math. Soc. 38 (1973), 499–502.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [137]
    P. Hill and H. Subramanian, "The freeness of a group based on a distributive lattice", Proc. Amer. Math. Soc. 51 (1975), 260–262.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [138]
    А.Г. Нурош [A.G. Kurosh], Теория Групп [The Theory of Groups], 3rd edition (Izdat. "Nauka", Moscow, 1967). (This edition has expanded coverage on abelian groups: pages 144–203 and 549–578.)Google Scholar
  13. [139]
    A.P. Mišina, "Abelian groups", Progress in Mathematics, 5, 1–37 (Plenum Press, New York, London, 1969).Google Scholar
  14. [140]
    A.P. Mishina, "Abelian groups", J. Soviet Math. 2 (1974), 239–263.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [141]
    G. Nöbeling, "Verallgemeinerung eines Satzes von Herrn E. Specker", Invent. Math. 6 (1968/69), 41–55.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [142]
    Robert W. Ritchie [Ed.], New Directions in Mathematics (Dartmouth College Mathematics Conference, 1961. Prentice Hall, Englewood Cliffs, New Jersey, 1963).Google Scholar
  17. [143]
    Saharon Shelah, "Infinite abelian groups, Whitehead problem and some constructions", Israel J. Math. 18 (1974), 243–256.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [144]
    Elbert A. Walker, "Ulm's theorem for totally projective groups", Proc. Amer. Math. Soc. 37 (1973), 387–392.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Irving Kaplansky
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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