Completely decomposable direct summands of torsion-free abelian groups of finite rank

Mader, Adolf; Schultz, Phill

doi:10.1090/proc/13732

Completely decomposable direct summands of torsion-free abelian groups of finite rank
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by Adolf Mader and Phill Schultz PDF

Proc. Amer. Math. Soc. 146 (2018), 93-96 Request permission

Abstract:

Let $A$ be a finite rank torsion-free abelian group. Then there exist direct decompositions $A=B\oplus C$ where $B$ is completely decomposable and $C$ has no rank 1 direct summand. In such a decomposition $B$ is unique up to isomorphism and $C$ is unique up to near-isomorphism.

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