J. Jir\'asko
On a generalization of QI-rings

Comment.Math.Univ.Carolinae 40,3 (1999) 441-446.

Abstract:In this paper rings for which every $s$-torsion quasi-injective module is weakly $s$-divisible for a hereditary preradical $s$ are characterized in terms of the properties of the corresponding lattice of the (hereditary) preradicals. In case of a stable torsion theory these rings coincide with $TQI$-rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning $QI$-rings obtained by J.S. Golan and S.R. L\'opez-Permouth in [12]. A characterization of the $QI$-property in the category $\sigma [M]$ then follows as a consequence.

Keywords: $s$-$QI$-rings, $s$-stable preradicals, weakly $s$-divisible modules, $s$-tight modules
AMS Subject Classification: 16D50, 16S90