1. A Generalization of Baer's Lemma.
- Creator:
- Dunkum, Molly
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Baer's Lemma, injective, representations of quivers, and torsion free covers
- Language:
- English
- Description:
- There is a classical result known as Baer's Lemma that states that an $R$-module $E$ is injective if it is injective for $R$. This means that if a map from a submodule of $R$, that is, from a left ideal $L$ of $R$ to $E$ can always be extended to $R$, then a map to $E$ from a submodule $A$ of any $R$-module $B$ can be extended to $B$; in other words, $E$ is injective. In this paper, we generalize this result to the category $q_{\omega }$ consisting of the representations of an infinite line quiver. This generalization of Baer's Lemma is useful in proving that torsion free covers exist for $q_{\omega }$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public