Five theorems on abelian groups

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
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
George M. Bergman, "Boolean rings of projection maps", J. London Math. Soc. (2) 4 (1972), 593–598.
Article MathSciNet MATH Google Scholar
Joel M. Cohen and Herman Gluck, "Stacked bases for modules over principal ideal domains", J. Algebra 14 (1970), 493–505.
Article MathSciNet MATH Google Scholar
Richard M. Dudley, "Unsolvable problems in mathematics" (Letter to the Editor), Science 191 (1976), 807–808.
Article Google Scholar
Paul C. Eklof, "Whitehead's problem is undecidable", Amer. Math. Monthly 83 (1976), 775–788.
Article MathSciNet MATH Google Scholar
László Fuchs, Infinite Abelian Groups, I (Pure and Applied Mathematics, 36. Academic Press, New York, London, 1970).
MATH Google Scholar
László Fuchs, Infinite Abelian Groups, II (Pure and Applied Mathematics, 36-II. Academic Press, New York, London, 1973).
MATH Google Scholar
Phillip A. Griffith, Infinite Abelian Group Theory (University of Chicago Press, Chicago, Illinois, London; 1970).
MATH Google Scholar
Paul Hill, "The additive group of commutative rings generated by idempotents", Proc. Amer. Math. Soc. 38 (1973), 499–502.
Article MathSciNet MATH Google Scholar
P. Hill and H. Subramanian, "The freeness of a group based on a distributive lattice", Proc. Amer. Math. Soc. 51 (1975), 260–262.
Article MathSciNet MATH Google Scholar
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
A.P. Mišina, "Abelian groups", Progress in Mathematics, 5, 1–37 (Plenum Press, New York, London, 1969).
Google Scholar
A.P. Mishina, "Abelian groups", J. Soviet Math. 2 (1974), 239–263.
Article MathSciNet MATH Google Scholar
G. Nöbeling, "Verallgemeinerung eines Satzes von Herrn E. Specker", Invent. Math. 6 (1968/69), 41–55.
Article MathSciNet MATH Google Scholar
Robert W. Ritchie [Ed.], New Directions in Mathematics (Dartmouth College Mathematics Conference, 1961. Prentice Hall, Englewood Cliffs, New Jersey, 1963).
Google Scholar
Saharon Shelah, "Infinite abelian groups, Whitehead problem and some constructions", Israel J. Math. 18 (1974), 243–256.
Article MathSciNet MATH Google Scholar
Elbert A. Walker, "Ulm's theorem for totally projective groups", Proc. Amer. Math. Soc. 37 (1973), 387–392.
MathSciNet MATH Google Scholar

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Department of Mathematics, University of Chicago, Chicago, Illinois, USA
Irving Kaplansky

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Irving Kaplansky
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M. F. Newman J. S. Richardson

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Kaplansky, I. (1978). Five theorems on abelian groups. In: Newman, M.F., Richardson, J.S. (eds) Topics in Algebra. Lecture Notes in Mathematics, vol 697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103121

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DOI: https://doi.org/10.1007/BFb0103121
Published: 30 December 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09103-5
Online ISBN: 978-3-540-35549-6
eBook Packages: Springer Book Archive

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