- Camillo's theorem on semihereditary polynomial rings
- Characterizations of hereditary rings
- Characterizations of quasi-Frobenius rings
- Characterizations of right nonsingular rings
- Characterizations of right perfect rings
- Characterizations of self-injective rings
- Characterizations of semiperfect rings
- Characterizations of semisimplicity
- Characterizations of von Neumann regular rings
- Commutative equivalents to von Neumann regularity
- Goldie's theorem on semisimple classical quotient rings
- Levy's characterization of almost-self-injective Noetherian rings
- Ore's theorem on the classical quotient ring of a domain