Abstract
A right [Formula: see text]-module [Formula: see text] is called a [Formula: see text]-module if, whenever [Formula: see text] and [Formula: see text] are submodules of [Formula: see text] with [Formula: see text] and [Formula: see text] there exist two direct summands [Formula: see text] and [Formula: see text] of [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text]. The class of [Formula: see text]-modules is a strict and simultaneous generalization of quasi-continuous, square-free and automorphism-invariant modules. In this paper we study the rings whose cyclics are [Formula: see text]-modules, extending many of the known results on the subject and providing new ones.
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