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A class of pure subgroups of completely decomposable abelian groups

Author: David M. Arnold
Journal: Proc. Amer. Math. Soc. 41 (1973), 37-44
MSC: Primary 20K25
MathSciNet review: 0325806
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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 [Enhancements On Off] (What's this?)

  • [1] D. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free Abelian groups (to appear).
  • [2] M. C. R. Butler, A class of torsion-free Abelian groups of finite rank, Proc. London Math. Soc. (3) 15 (1965), 680-698. MR 36 #1532. MR 0218446 (36:1532)
  • [3] T. B. Cruddis, On a class of torsion-free Abelian groups, Proc. London Math. Soc. (3) 21 (1970), 243-276. MR 42 #6104. MR 0271221 (42:6104)
  • [4] L. Fuchs, Abelian groups, Akad. Kiadó, Budapest, 1958; republished by Internat. Series of Monos on Pure and Appl. Math., Pergamon Press, New York, 1960. MR 21 #5672; 22 #2644. MR 0111783 (22:2644)
  • [5] -, Infinite Abelian groups. Vol. I, Pure and Appl. Math., vol. 36, Academic Press, New York, 1970. MR 41 #333. MR 0255673 (41:333)

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Keywords: Torsion free abelian groups of finite rank, completely decomposable groups
Article copyright: © Copyright 1973 American Mathematical Society

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