Abstract
We examine when versions of the Krull-Schmidt property hold for (1) direct sums of ideals of integral domains, (2) direct sums of indecomposable submodules of finitely generated free modules, and (3) direct sums of rank one torsion-free modules. Our main results are formulated for modules over h-local integral domains without recourse to finite generation for the modules. This leads to some new results for Krull-Schmidt properties of modules over Noetherian and Prufer domains.
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