ON SMALL INJECTIVE, SIMPLE-INJECTIVE AND QUASI-FROBENIUS RINGS.

Let R be a ring. A right ideal I of R is called small in R if I + K ≠ R for every proper right ideal K of R. A ring R is called right small finitely injective (briefly, SF-injective) (resp., right small principally injective (briefly, SP-injective) if every homomorphism from a small and finitely generated right ideal (resp., a small and principally right ideal) to RR can be extended to an endomorphism of RR. The class of right SF-injective and SP-injective rings are broader than that of right small injective rings (in [15]). Properties of right SF-injective rings and SP-injective rings are studied and we give some characterizations of a QF-ring via right SF-injectivity with ACC on right annihilators. Furthermore, we answer a question of Chen and Ding. [ABSTRACT FROM AUTHOR]