Vol. LXXVIII, 2 (2009)
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  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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