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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 27 Sep 2017Embargo end date: 01 Jan 2017 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 146, pages 93-96 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Mader, Adolf; Schultz, Phill;

doi: 10.1090/proc/13732 , 10.48550/arxiv.1701.02460

arXiv: 1701.02460

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

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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 $C$ unique up to near-isomorphism.

6 pages

Related Organizations

University of Western Australia
Australia
University of Hawaii System
United States
University of Hawaii at Manoa
United States
University of Hawaiʻi Sea Grant
United States

Keywords

20K15, 20K25, FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory

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