# Property: (right/left) principally injective

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

## Resources for learning about this property:

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

## Metaproperties:

This property has the following metaproperties

- stable under products
- stable under finite products

This property

**does not** have the following metaproperties