Classification theory of abelian groups. I. Balanced projectives

Warfield, R. B.

doi:10.1090/S0002-9947-1976-0422455-X

Classification theory of abelian groups. I. Balanced projectives
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by R. B. Warfield

Trans. Amer. Math. Soc. 222 (1976), 33-63

DOI: https://doi.org/10.1090/S0002-9947-1976-0422455-X

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Abstract:

We introduce in this paper a class of Abelian groups which includes the torsion totally projective groups and those torsion-free groups which are direct sums of groups of rank one. Characterizations of the groups in this class are given, and a complete classification theorem, in terms of additive numerical invariants, is proved.

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Classification theorems for infinite Abelian groups