p. 161 - 172 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 [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. Keywords: SP(SF)-injective ring; P(F)-injective; mininjective ring; simple-injective; simple-FJ-injective. AMS Subject classification: Primary: 16D50, 16D70, 16D80 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |