Abstract
In recent work the authors introduced the notion of near-isomorphism for torsion-free abelian groups of infinite rank. In a natural way this concept extends the classical definition of near-isomorphism in the finite rank case. We prove some further properties of this notion and introduce the new concept of bounded near-isomorphism which is a stronger form of near-isomorphism. As an application we study bounded near-isomorphic bounded completely decomposable abelian groups (bcd-groups). It is shown that bcd-groups allow a theory that is very similar to the theory of almost completely decomposable groups with respect to bounded near-isomorphism.
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The first author is grateful to the German Academic Exchange Service (DAAD) for their support of this research.
The second author is grateful to the German Research Foundation for their support of this research within the project STR 627/14-1.
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Blagoveshchenskaya, E., Strüngmann, L. Near-isomorphism for bounded completely decomposable groups. Isr. J. Math. 241, 277–299 (2021). https://doi.org/10.1007/s11856-021-2096-2
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DOI: https://doi.org/10.1007/s11856-021-2096-2