On Modules Whose Singular Subgenerated Modules Are Weakly Injective

摘要

Rings over which every singular right module is injective (briefly,right SI-rings) were introduced and investigated by Goodearl. Weakly injective modules, as a generalization of injective modules, were introduced by Jain and modules are weakly injective, which we call SwI-rings. This concept is extended to SwI-modules, i.e., modules whose singular subgenerated modules are weakly injective. Several characterizations and properties of SwI-rings and SwI-modules are obtained which generalize some earlier known results on SI-rings and weakly semisimple rings.