Module theory MOC Simple module A (left) module 𝑀 ∈𝑅𝖬𝗈𝖽 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 #state/tidy | #lang/en | #SemBr