Geodesic
On (co)pure Baer injective modules
Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 219-226

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For a given class of $R$-modules $\mathcal{Q}$, a module $M$ is called $\mathcal{Q}$-copure Baer injective if any map from a $\mathcal{Q}$-copure left ideal of $R$ into $M$ can be extended to a map from $R$ into $M$. Depending on the class $\mathcal{Q}$, this concept is both a dualization and a generalization of pure Baer injectivity. We show that every module can be embedded as $\mathcal{Q}$-copure submodule of a $\mathcal{Q}$-copure Baer injective module. Certain types of rings are characterized using properties of $\mathcal{Q}$-copure Baer injective modules. For example a ring $R$ is $\mathcal{Q}$-coregular if and only if every $\mathcal{Q}$-copure Baer injective $R$-module is injective.
Keywords: $\mathcal{Q}$-copure submodule, $\mathcal{Q}$-copure Baer injective module
Mots-clés : pure Baer injective module. 
@article{ADM_2021_31_2_a3,
     author = {M. F. Hamid},
     title = {On (co)pure {Baer} injective modules},
     journal = {Algebra and discrete mathematics},
     pages = {219--226},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a3/}
}
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M. F. Hamid. On (co)pure Baer injective modules. Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a3/