= Finite uniform decomposition of a Noetherian module
Every nonzero <Noetherian module> contains a <uniform module>: otherwise repeatedly split a nonuniform nonzero submodule into two disjoint nonzero submodules, retaining one and collecting the other, to build an infinite direct sum. Repeatedly adding a uniform submodule disjoint from the current finite sum must likewise stop. The final finite sum is an <essential submodule>, since any disjoint nonzero submodule would allow another addition.
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