Almost completely decomposable torsion free abelian groups
E. L. Lady
Proc. Amer. Math. Soc. 45 (1974), 41-47
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Abstract: A finite rank torsion free abelian group is almost completely decomposable if there exists a completely decomposable subgroup with finite index in . The minimum of over all completely decomposable subgroups of is denoted by . An almost completely decomposable group has, up to isomorphism, only finitely many summands. If is a prime power, then the rank 1 summands in any decomposition of as a direct sum of indecomposable groups are uniquely determined. If and are almost completely decomposable groups, then the following statements are equivalent: (i) for some finite rank torsion free abelian group . (ii) and contains a subgroup isomorphic to such that is finite and prime to . (iii) where is isomorphic to a completely decomposable subgroup with finite index in .
M. Arnold and E.
L. Lady, Endomorphism rings and direct sums of
torsion free abelian groups, Trans. Amer. Math.
Soc. 211 (1975),
225–237. MR 0417314
(54 #5370), http://dx.doi.org/10.1090/S0002-9947-1975-0417314-1
Fuchs, Infinite abelian groups. Vol. I, Pure and Applied
Mathematics, Vol. 36, Academic Press, New York, 1970. MR 0255673
- D. M. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free abelian groups, Trans. Amer. Math. Soc. (to appear). MR 0417314 (54:5370)
- L. Fuchs, Infinite abelian groups. Vol. I, Pure and Appl. Math., vol. 36, Academic Press, New York, 1970 and 1973. MR 41 #333. MR 0255673 (41:333)
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