ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXV, 2 (2006)
p. 199 - 208
On generalizations of injectivity
Le Duc Thoang and Le Van Thuyet

Abstract.  A ring R is called right GP-injective if for every nonzero element a in R, there exists a positive integer n such that an ¹ 0 and any right R -homomorphism of anR into R can be extended to one of R into R . A ring R is called right FSG if every finitely generated cofaithful right R-module is a generator in Mod-R . In this paper, we give some characterizations of PF rings, QF rings via GP-injective rings, FSG rings.

Keywords.  GP-injective ring, quasi-Frobenius ring, QF-2 ring, FPF-ring, FSG-ring, uniform dimension.

AMS Subject classification.  Primary: 16D50, 16D70, 16D80.
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