stylistic:style_transfer, structural:reformatting
Theorem D (modules)

Let M {\displaystyle M} be a module, N {\displaystyle N} a submodule of M {\displaystyle M}. There is a bijection between the submodules of M {\displaystyle M} that contain N {\displaystyle N} and the submodules of M / N {\displaystyle M/N}. The correspondence is given by A ↔ A / N {\displaystyle A\leftrightarrow A/N} for all A ⊇ N {\displaystyle A\supseteq N}. This correspondence commutes with the processes of taking sums and intersections (i.e., is a lattice isomorphism between the lattice of submodules of M / N {\displaystyle M/N} and the lattice of submodules of M {\displaystyle M} that contain N {\displaystyle N}).