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Homemodule of finite rank

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# module of finite rank

Let $M$ be a module, and let $E(M)$ be the injective hull of $M$. Then we say that $M$ has finite rank if $E(M)$ is a finite direct sum of indecomposable submodules.

This turns out to be equivalent to the property that $M$ has no infinite direct sums of nonzero submodules.

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