Geodesic
On a generalization of $QI$-rings
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 441-446

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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.
Classification : 16D50, 16N80, 16S90
Keywords: $s$-$QI$-rings; $s$-stable preradicals; weakly $s$-divisible modules; $s$-tight modules 
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     title = {On a generalization of $QI$-rings},
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     pages = {441--446},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a3/}
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Jirásko, J. On a generalization of $QI$-rings. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 441-446. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a3/