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 R can be extended
to an endomorphism of _{R}R. 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.
_{R}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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