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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A class of pure subgroups of completely decomposable abelian groups
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by David M. Arnold PDF
Proc. Amer. Math. Soc. 41 (1973), 37-44 Request permission

Abstract:

Direct sum decompositions of the class of pure subgroups of finite rank completely decomposable torsion free abelian groups with typesets of cardinality at most 4 are considered. In certain cases, the indecomposable groups are classified, resulting in new proofs of several theorems by T. B. Cruddis.
References
    D. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free Abelian groups (to appear).
  • M. C. R. Butler, A class of torsion-free abelian groups of finite rank, Proc. London Math. Soc. (3) 15 (1965), 680–698. MR 218446, DOI 10.1112/plms/s3-15.1.680
  • T. B. Cruddis, On a class of torsion-free abelian groups, Proc. London Math. Soc. (3) 21 (1970), 243–276. MR 271221, DOI 10.1112/plms/s3-21.2.243
  • L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783
  • László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 41 (1973), 37-44
  • MSC: Primary 20K25
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0325806-2
  • MathSciNet review: 0325806