Definition: All finitely generate right ideals are free and of unique rank

- P. M. Cohn. Free ideal rings and localization in general rings. (2006) @ .

- passes to quotient rings (Counterexample: $R_{ 49 }$ is a homomorphic image of $R_{ 27 }$)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)

Rings

Legend

- = has the property
- = does not have the property
- = information not in database