Quasi-Direct Decompositions of Torsion-Free Abelian Groups of Infinite Rank.

L. Fuchs; G. Viljoen

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On Direct Decomposition of Torsion Free Abelian Groups.

Bjarni Jonsson (1959)

Mathematica Scandinavica

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Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

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An exact sequence $0 \to A \to B \to C \to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $0 \to 𝐐 \otimes Hom (X, A) \to 𝐐 \otimes Hom (X, B) \to 𝐐 \otimes Hom (X, C) \to 0$ is exact for all rank-1 torsion-free abelian groups $X$ . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise...

Self-cancellation of torsion-free Abelian groups of finite rank.

Blazhenov, A.V. (2002)

Zapiski Nauchnykh Seminarov POMI

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The automorphism groups and endomorphism rings of torsion-free abelian groups of rank two

M. Król

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CONTENTS§ 1. Introduction.......................................................................................................................................... 5§ 2. Definitions and lemmas................................................................................................................... 7§ 3. Theorem on the isomorphism of subdirect sums with the same kernels............................. 15§ 4. The group of automorphisms of a torsion-free abelian group of rank two................................