Geodesic
Basic submodules of modules over right noetherian serial rings.~I
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 129-143

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It is proved that any right module over right noetherian serial ring $R$ contains a basic submodule. The structure of submodules of an indecomposable pure-injective $R$-module is investigated. 
@article{ZNSL_2000_272_a5,
     author = {A. I. Generalov and I. M. Zilberbord},
     title = {Basic submodules of modules over right noetherian serial {rings.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--143},
     publisher = {mathdoc},
     volume = {272},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a5/}
}
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A. I. Generalov; I. M. Zilberbord. Basic submodules of modules over right noetherian serial rings.~I. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 129-143. http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a5/