Definition: (right principally injective) homomorphisms from principal right ideals of the ring into the ring extend to endomorphisms of the ring

- E. A. Rutter and Jr. Rings with the principal extension property. (1975) @ .
- W. K. Nicholson and M. F. Yousif. Principally injective rings. (1995) @ .

- stable under products
- stable under finite products

- passes to polynomial rings (Counterexample: $R_{ 7 }$)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)
- passes to quotient rings (Counterexample: $R_{ 84 }$ is a homomorphic image of $R_{ 122 }$)

Rings

Legend

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