Abstract
Carl Faith in 2003 introduced and investigated an interesting class of rings over which every cyclic right module has Σ-injective injective hull (abbr., right CSI-rings) [5]. Inspired by this we investigate rings over which every cyclic right R-module has a projective Σ-injective injective hull. We show that a ring R satisfies this condition if and only if R is right artinian, the injective hull of R R is projective and every simple right R-module is embedded in R R . We also characterize right artinian rings in terms of injective faithful right ideals and right CSI-rings.
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