Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Cancellation of direct sums of countable abelian -groups

Author(s): Rüdiger Göbel; Warren May
Journal: Proc. Amer. Math. Soc. 131 (2003), 2705-2710.
MSC (2000): Primary 20K10, 20K21, 20K25
Posted: January 15, 2003
MathSciNet review: 1974325
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Abstract: Let $B \oplus A_{1} = C \oplus A_{2}$ be abelian groups where $B \cong C$ is a direct sum of countable -groups. A condition is given on the Ulm-Kaplansky -invariants of $B, A_{1}$ and $A_{2}$ such that $A_{1} \cong A_{2}$ .

References:

1.: P. Crawley, The cancellation of torsion abelian groups in direct sums, J. Algebra 2 (1965) 432-442. MR 32:5732
2.: L. Fuchs, Infinite Abelian Groups, Vol. I, Vol. II, Academic Press, New York 1970, 1973. MR 41:333, MR 50:2362
3.: R. Göbel, W. May, Modular group algebras of $\aleph_{1}$ -separable -groups, to appear.

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