Module theory MOC Submodule Let be a (left) module. A submodule is a module under the same operations, #m/def/module i.e. is a subgroup such that for any and . Thus a submodule is an invariant subspace under the carried representation of (see invariant subspace). Examples Let be an ideal. Then is an -submodule of . #state/tidy | #lang/en | #SemBr