Geodesic
On P-extending Modules
Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2 
M. A. Kamal; O. A. Elmnophy. On P-extending Modules. Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a13/
@article{AMUC_2005_74_2_a13,
     author = {M. A. Kamal and O. A. Elmnophy},
     title = {On {P-extending} {Modules}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2005},
     volume = {74},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a13/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let R be a ring. A right R -module M is called quasi-principally injective if it is M -principally injective.In this paper, we give some characterizations and properties of principally injective modules, which generalize results of Nicholson and Yousif. For a quasi-principally injective module M , we show: 1. For isomorphic submodules H , K of M , we have SH = SK , where S is the endomorphism ring of M . 2. M has ( PC 2 ), and consequently has ( PC 3 ). We characterize when a direct sum of P-extending modules is P-extending, and when a direct sum of a P-extending module and a semi-simple module is P-extending. We also characterize when a direct sum of FP-extending modules is FP-extending. Finally, we discuss when a direct sum of P-extending modules with relatively EC-injective is P-extending.