Geodesic
Rings all of whose torsion quasi-injective modules are injective
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 219-227

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper it is assumed that rings are associative, have the identity element, and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R-modules, and for each left R-module M, E(M) (resp. J(M)) will represent the injective hull (resp. Jacobson radical) of M. Also, for a module M, A ⊆' M will mean that A is an essential submodule of M, and Z(M) denotes the singular submodule of M. M is called singular if Z(M) = M, and it is called non-singular in case Z(M) = 0. For fundamental definitions and results related to torsion theories, we refer to [12] and [14]. In this paper we shall deal mainly with Goldie torsion theory. Recall that a pair (G, F) of classes of left R-modules is known as Goldie torsion theory if G is the smallest torsion class containing all modules B/A, where A ⊆' B, and the torsion free class F is precisely the class of non-singular modules. 
Ahsan, J.; Enochs, E. Rings all of whose torsion quasi-injective modules are injective. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 219-227. doi: 10.1017/S0017089500005644
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