Proceedings of the American Mathematical Society · 1981 · 16 citations · 4 references
Natural SciencesMathematicsDiscrete MathematicsNumber TheorySet TheoryAbstract AlgebraCountability AxiomsGroup TheoryAbelian Categories
Three different definitions of the third axiom of counlability for abelian ^-groups are shown to be equivalent. The main interest in this stems from the fact that the third axiom of countability characterizes one of the most important classes of abelian groups. Moreover, the equivalence of two of these definitions validates the proof of Theorem 67 in P. Griffith's Infinite abelian group theory.
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Homology and direct sums of countable Abelian groups
R. J. Nunke · Mathematische Zeitschrift · 1967 · 109 citations
On the classification of abelian groups
Paul Hill · Periodica Mathematica Hungarica · 2014 · 19 citations