Homological Independence of Injective Hulls of Simple Modules Over Certain Noncommutative Rings

Abstract

We study noncommutative rings $R$ having the property that there is no nonzero homomorphism between injective hulls of nonisomorphic simple left $R$-modules. For rings satisfying the condition that the torsion theory cogenerated by the injective hull of a simple left $R$-module is always jansian, we characterize this property in terms of the lattice of torsion theories on the category of left $R$-modules.