Abstract
We apply minimal weakly generating sets to study the existence of Add(U-R)-covers for a uniserial module U-R. If U-R is a uniserial right module over a ring R, then S := End(U-R) 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 U-R that are not surjective.
We prove that if U-R is either finitely generated, or artinian, or I subset of K, then the class Add(U-R) is covering if and only if it is closed under direct limit. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples. (C) 2020 Elsevier Inc.
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