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On small injective, simple-injective and quasi-Frobenius rings
Le van Thuyet and Truong Cong Quynh
Received: January 16, 2007; Revised: February 18, 2009; Accepted: February 16, 2009
Abstract. 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 ). 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.
Keywords: SP(SF)-injective ring; P(F)-injective; mininjective ring; simple-injective; simple-FJ-injective.
AMS Subject classification: Primary: 16D50, 16D70, 16D80
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