Abstract
Carl Faith (2003) introduced and investigated an interesting class of rings over which every cyclic right module has Σ-injective injective hull (abbr., right CSI-rings). Inspired by this we investigate rings over which every cyclic right R-module has a Σ-extending injective hull. We call such rings right CSE-rings and show that the class of right CSE-rings and that of right CSI-rings coincide. We also use other hulls of cyclic modules to define other classes of rings, and investigate their structure. We prove, among others, that a ring R is right QI if and only if the quasi-injective hull of each cyclic right module is Σ-injective.
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