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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - M. F. Hamid
TI  - On (co)pure Baer injective modules
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 219
EP  - 226
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a3/
LA  - en
ID  - ADM_2021_31_2_a3
ER  - 
%0 Journal Article
%A M. F. Hamid
%T On (co)pure Baer injective modules
%J Algebra and discrete mathematics
%D 2021
%P 219-226
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a3/
%G en
%F ADM_2021_31_2_a3
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/

[1] Iuliu Crivei, “$s$-Pure submodules”, Int. J. Math. Math. Sci., 2005 (2005), 491–497 | DOI | MR | Zbl

[2] John Dauns, Modules and Rings, Cambridge University Press, 1994 | MR | Zbl

[3] Nada M. Al Thani, “Pure Baer injective modules”, Int. J. Math. Math. Sci., 20 (1997), 529–538 | DOI | MR | Zbl

[4] Robert Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, 1991 | MR | Zbl