Cancellation of direct sums of countable abelian $p$-groups
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- by Rüdiger Göbel and Warren May PDF
- Proc. Amer. Math. Soc. 131 (2003), 2705-2710 Request permission
Abstract:
Let $B \oplus A_{1} = C \oplus A_{2}$ be abelian groups where $B \cong C$ is a direct sum of countable $p$-groups. A condition is given on the Ulm-Kaplansky $p$-invariants of $B, A_{1}$ and $A_{2}$ such that $A_{1} \cong A_{2}$.References
- Peter Crawley, The cancellation of torsion abelian groups in direct sums, J. Algebra 2 (1965), 432–442. MR 188293, DOI 10.1016/0021-8693(65)90004-9
- Walter Leighton and W. T. Scott, A general continued fraction expansion, Bull. Amer. Math. Soc. 45 (1939), 596–605. MR 41, DOI 10.1090/S0002-9904-1939-07046-8
- R. Göbel, W. May, Modular group algebras of $\aleph _{1}$-separable $p$-groups, to appear.
Additional Information
- Rüdiger Göbel
- Affiliation: Fachbereich 6, Mathematik und Informatik, Universität Essen, Universitätsstr. 3, 45117 Essen, Germany
- Email: R.Goebel@Uni-Essen.De
- Warren May
- Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
- Email: may@math.arizona.edu
- Received by editor(s): January 25, 2002
- Received by editor(s) in revised form: April 13, 2002
- Published electronically: January 15, 2003
- Communicated by: Stephen D. Smith
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2705-2710
- MSC (2000): Primary 20K10, 20K21, 20K25
- DOI: https://doi.org/10.1090/S0002-9939-03-06817-5
- MathSciNet review: 1974325