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Let R be an integral domain. All modules under discussion are torsion free unital left R-modules.     An R-module is completely decomposable if it is the direct sum of rank 1 submodules.     An R-...

Let $G$ be an abelian group and $G=\bigoplus_{i=1}^t{{\Bbb{Z}}_{p_i}^{n_i}}^{(\Lambda_i)}$ where each $\Lambda_i$ is a set (at least one of $\Lambda_i$ is infinite). Since $G_{\Bbb{Z}}$ is a finite-...