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.

中文翻译：

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有界完全可分解基团的近同构

在最近的工作中，作者介绍了无限同构的无扭转阿贝尔族的近似同构概念。这种概念自然地扩展了有限秩情况下的近似同构的经典定义。我们证明了该概念的一些其他性质，并介绍了有界近同构的新概念，它是近同构的更强形式。作为一种应用，我们研究了有界近同构有界完全可分解的阿贝尔群（bcd-groups）。结果表明，对于有界的近同构，bcd-groups允许的理论与几乎完全可分解的groups的理论非常相似。