Geodesic
Self-injective rings and endomorphisms of free modules
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 533-540.

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It is shown that the ring of endomorphisms of an arbitrary free $R$-module is right self-injective if and only if $R$ is quasi-Frobenius. 
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     author = {V. I. Gemintern},
     title = {Self-injective rings and endomorphisms of free modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {533--540},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a2/}
}
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V. I. Gemintern. Self-injective rings and endomorphisms of free modules. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 533-540. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a2/