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Paper IPM / M / 16409  


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, twosided) 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 ⊂ 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.
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