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) @ .


This property has the following metaproperties
  • stable under products
  • stable under finite products
This property does not have the following metaproperties