Let $R$ be a commutative local ring and $M$ be an $R$-module. To determine the structure of $M$, does it suffice to determine the structure of all indecomposable summands of $M$ and then say that $M$ is a direct sum of this submodules?
Thank you.
2026-03-30 01:53:11.1774835591
Does every module over a commutative local ring direct sum of all its indecomposable submodules?
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