Abstract
A left [Formula: see text]-module [Formula: see text] is said to be left singly injective if [Formula: see text] for any cyclic submodule [Formula: see text] of any finitely generated free left [Formula: see text]-module [Formula: see text]. In this paper, we study the notion of singly injective modules which is generalization of injective modules and absolutely pure modules. In this direction, we give conditions which guarantee that each singly injective left [Formula: see text]-module is either injective or absolutely pure. Finally, we study rings whose simple modules are singly injective (SSI-rings).
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