[[Module theory MOC]]
# Simple module

 A (left) [[module]] $M \in \lMod R$ is (left) **simple** or **irreducible** iff it has no nontrivial proper [[submodule]]. #m/def/module 

## Properties

- [[Schur's lemma]] states that any nonzero homomorphism between simple modules is an isomorphism.


## See also

- [[Semisimple module]]

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