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Paper   IPM / M / 16409
School of Mathematics
  Title:   Covering classes and uniserial modules
  Author(s):  Zahra Nazemian (Joint with A. Facchini and P. Prihoda)
  Status:   To Appear
  Journal: J. Algebra
  Supported by:  IPM
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 IK, 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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