Abstract
We apply minimal weakly generating sets to study the existence of Add(UR)-covers for a uniserial module UR. If UR is a uniserial right module over a ring R, then S:=End(UR) has at most two maximal (right, left, two-sided) ideals: one is the set I of all endomorphisms that are not injective, and the other is the set K of all endomorphisms of UR that are not surjective. We prove that if UR is either finitely generated, or artinian, or I⊂K, then the class Add(UR) is covering if and only if it is closed under direct limit. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples.
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