A Generalization of Simple-Injective Rings

Abstract

A ring R is called right 2-simple J-injective if, for every 2-generated right ideal I ⊆ J(R), every R-linear map from I to R with simple image extends to R. The class of right 2-simple J-injective rings is broader than that of right 2-simple injective rings and right simple J-injective rings. Right 2-simple J-injective right Kasch rings are studied, several conditions under which right 2-simple J-injective rings are QF-rings are given.