Geodesic
Completion of modules over right noetherian serial rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 8, Tome 281 (2001), pp. 170-185

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We define a linear topology on arbitrary right module over right noetherian serial ring $R$ that allows to describe reduced pure-injective $R$-modules as modules which are complete in this topology. Using the operation of completion we describe pure-injective envelope of any right $R$-module. 
@article{ZNSL_2001_281_a7,
     author = {A. I. Generalov and I. M. Zilberbord},
     title = {Completion of modules over right noetherian serial rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {170--185},
     publisher = {mathdoc},
     volume = {281},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_281_a7/}
}
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A. I. Generalov; I. M. Zilberbord. Completion of modules over right noetherian serial rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 8, Tome 281 (2001), pp. 170-185. http://geodesic.mathdoc.fr/item/ZNSL_2001_281_a7/