Czechoslovak Mathematical Journal

, Volume 59, Issue 1, pp 241–247 | Cite as

A generalization of Baer’s Lemma



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.


Baer’s Lemma injective representations of quivers torsion free covers 

MSC 2000

13D30 18G05 


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    R. Baer: Abelian groups that are direct summands of every containing abelian group. Bull. Amer. Math. Soc. 46 (1940), 800–806.CrossRefMathSciNetGoogle Scholar
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    E. Enochs: Torsion free covering modules. Proc. Amer. Math. Soc. 14 (1963), 884–889.MATHCrossRefMathSciNetGoogle Scholar
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    M. Dunkum Wesley: Torsion free covers of graded and filtered modules. Ph.D. thesis, University of Kentucky, 2005.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Department of MathematicsWestern Kentucky UniversityBowling GreenU.S.A.

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