A Generalization of Baer's Lemma
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 1, page 241-247
- ISSN: 0011-4642
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topDunkum, Molly. "A Generalization of Baer's Lemma." Czechoslovak Mathematical Journal 59.1 (2009): 241-247. <http://eudml.org/doc/37920>.
@article{Dunkum2009,
abstract = {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 $q_\{\omega \}$.},
author = {Dunkum, Molly},
journal = {Czechoslovak Mathematical Journal},
keywords = {Baer's Lemma; injective; representations of quivers; torsion free covers; Baer's lemma; injective; representation of quivers; torsion free cover},
language = {eng},
number = {1},
pages = {241-247},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Generalization of Baer's Lemma},
url = {http://eudml.org/doc/37920},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Dunkum, Molly
TI - A Generalization of Baer's Lemma
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 241
EP - 247
AB - 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 $q_{\omega }$.
LA - eng
KW - Baer's Lemma; injective; representations of quivers; torsion free covers; Baer's lemma; injective; representation of quivers; torsion free cover
UR - http://eudml.org/doc/37920
ER -
References
top- Baer, R., 10.1090/S0002-9904-1940-07306-9, Bull. Amer. Math. Soc. 46 800-806 (1940). (1940) Zbl0024.14902MR0002886DOI10.1090/S0002-9904-1940-07306-9
- Enochs, E., 10.1090/S0002-9939-1963-0168617-7, Proc. Amer. Math. Soc. 14 884-889 (1963). (1963) Zbl0116.26003MR0168617DOI10.1090/S0002-9939-1963-0168617-7
- Wesley, M. Dunkum, Torsion free covers of graded and filtered modules, Ph.D. thesis, University of Kentucky (2005). (2005) MR2707058
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