On the Splitting of Modules and Abelian Groups
1974 ◽
Vol 26
(1)
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pp. 68-77
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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.
1992 ◽
Vol 52
(2)
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pp. 219-236
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1989 ◽
Vol 39
(1)
◽
pp. 21-24
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1969 ◽
Vol 12
(4)
◽
pp. 475-478
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1969 ◽
Vol 12
(4)
◽
pp. 479-480
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Keyword(s):