2-Simple Injective Rings

A ring R is called right 2-simple injective if, for every 2-generated right ideal I of R, every R-linear map from I to R with simple image extends to R. The class of right 2-simple injective rings is broader than that of right simple injective rings and right 2-injective rings . We study characterizations and properties of right 2-simple injective rings, several conditions under which right 2-simple injective rings are QF-rings are given.