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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Classification theory of abelian groups. I. Balanced projectives

Author: R. B. Warfield
Journal: Trans. Amer. Math. Soc. 222 (1976), 33-63
MSC: Primary 20K40
MathSciNet review: 0422455
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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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Keywords: Ulm’s theorem, totally projective groups, completely decomposable groups, invariants for Abelian groups, modules over a discrete valuation ring, extension of homomorphisms and isomorphisms, relative projectives, additive categories, decompositions of groups
Article copyright: © Copyright 1976 American Mathematical Society