A generalization of Baer’s Lemma
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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 ω 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 ω.
KeywordsBaer’s Lemma injective representations of quivers torsion free covers
MSC 200013D30 18G05
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- M. Dunkum Wesley: Torsion free covers of graded and filtered modules. Ph.D. thesis, University of Kentucky, 2005.Google Scholar