- Andrunakievič's theorem on subdirect representations of reduced rings
- Artin - Wedderburn theorem
- Frobenius' theorem
- Jacobson density theorem
- Kaplansky's theorem on modules of right hereditary rings
- Kaplansky's theorem on PI algebras
- Structure of Noetherian distributive rings
- Structure of self-injective von Neumann regular rings
- Uniserial Noetherian rings
- Wedderburn's little theorem