Geodesic
Annihilator conditions in endomorphism rings of modules
Matematičeskie zametki, Tome 16 (1974) no. 6, pp. 933-942.

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The concepts of an intrinsically projective module and an intrinsically injective module are introduced and their connection with the presence of annihilator conditions in the endomorphism ring of a module is explained. It is shown that a ring $R$ is quasi-Frobenius if and only if in the endomorphism ring of any fully projective (or any fully injective) $R$-module it is true that $r(l(I))=I$ and $l(r(J))=J$ for all finitely generated right ideals $I$ and finitely generated left ideals $J$. 
@article{MZM_1974_16_6_a9,
     author = {G. M. Brodskii},
     title = {Annihilator conditions in endomorphism rings of modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {933--942},
     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_6_a9/}
}
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G. M. Brodskii. Annihilator conditions in endomorphism rings of modules. Matematičeskie zametki, Tome 16 (1974) no. 6, pp. 933-942. http://geodesic.mathdoc.fr/item/MZM_1974_16_6_a9/