Geodesic
On small injective, simple-injective and quasi-Frobenius rings
Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 2 
Le van Thuyet; Truong Cong Quynh. On small injective, simple-injective and quasi-Frobenius rings. Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2009_78_2_a0/
@article{AMUC_2009_78_2_a0,
     author = {Le van Thuyet and Truong Cong Quynh},
     title = {On small injective, simple-injective and {quasi-Frobenius} rings},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2009},
     volume = {78},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2009_78_2_a0/}
}
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Let R be a ring. A right ideal I of R is called small in R if I + K 1 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.