information:filtering
Generalization

For an R -module A, a maximal submodule M of A is a submodule M ≠ A satisfying the property that for any other submodule N, M ⊆ N ⊆ A implies N = M or N = A. Equivalently, M is a maximal submodule if and only if the quotient module A / M is a simple module. The maximal right ideals of a ring R are exactly the maximal submodules of the module R.