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| Paper IPM / M / 16409 |
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| Abstract: | |
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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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