Geodesic
Purities and pure injective modules over serial right noetherian rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 214-232

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It is proved that any submodule of direct sum of some family of finitely generated right modules over serial right noetherian ring $R$ is also a direct sum of finitely generated modules. With use of reduction to serial right hereditary rings we obtained a new description of all indecomposable pure injective noninjective right modules over serial right noetherian rings. 
@article{ZNSL_2002_289_a11,
     author = {I. M. Zilberbord},
     title = {Purities and pure injective modules over serial right noetherian rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {214--232},
     publisher = {mathdoc},
     volume = {289},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a11/}
}
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I. M. Zilberbord. Purities and pure injective modules over serial right noetherian rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 214-232. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a11/