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Indecomposable module
In abstract algebra, a module is defined to be indecomposable if it is non-zero and cannot be written as a direct sum of two non-zero submodules. In many situations, all modules of interest can be written as direct sums of indecomposable ones; the indecomposable modules can then be thought of as the "basic building blocks", the only objects that need to be studied.
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