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arXiv · 2001.03085

Covering classes and uniserial modules

Alberto Facchini·Zahra Nazemian·Pavel Prihoda
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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 $I \subset K$, 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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Alberto Facchini, Zahra Nazemian, Pavel Prihoda. 2020-01-09. Covering classes and uniserial modules. https://arxiv.org/abs/2001.03085

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