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.

Covering classes and uniserial modules

Facchini A.
;
2021

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3381737
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