Geodesic
A Generalization of Baer's Lemma
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 241-247 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $q_{\omega }$.
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 $q_{\omega }$.
Classification : 13D30, 16G20, 18G05
Keywords: Baer's Lemma; injective; representations of quivers; torsion free covers 
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     author = {Dunkum, Molly},
     title = {A {Generalization} of {Baer's} {Lemma}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {241--247},
     year = {2009},
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     zbl = {1224.13015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a16/}
}
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Dunkum, Molly. A Generalization of Baer's Lemma. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 241-247. http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a16/