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On the Splitting of Modules and Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Paul Hill
Paul Hill*
Affiliation:
Florida State University, Tallahassee, Florida
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In a fundamental paper on torsion-free abelian groups, R. Baer [1] proved that the group P of all sequences of integers with respect to componentwise addition is not free. This means precisely that P is not a direct sum of infinite cyclic groups. However, E. Specker proved in [9] that P has the property that any countable subgroup is free. Since an infinite abelian group G is called -free if each subgroup of rank less than is free, these results are equivalent to: P is -free but not free.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 68 - 77
Copyright
Copyright © Canadian Mathematical Society 1974

References

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