Geodesic
Decomposability of modules into a direct sum of ideals
Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 187-193.

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It is shown that each left $R$ module is isomorphic to a direct sum of left ideals of the ring $R$ if and only if $R$ is quasi-Frobenius and generalized uniserial. 
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     author = {L. A. Skornyakov},
     title = {Decomposability of modules into a direct sum of ideals},
     journal = {Matemati\v{c}eskie zametki},
     pages = {187--193},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a2/}
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L. A. Skornyakov. Decomposability of modules into a direct sum of ideals. Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 187-193. http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a2/