Geodesic
Net subrings of generalized matrix rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 184-198 
A. V. Yakovlev. Net subrings of generalized matrix rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 184-198. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a16/
@article{ZNSL_1994_211_a16,
     author = {A. V. Yakovlev},
     title = {Net subrings of generalized matrix rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--198},
     year = {1994},
     volume = {211},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a16/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Lambda$ be a ring with the following properties: (a) $\Lambda$ is a direct sum of left ideals $P_1,\dots,p_n$; (b) every nontrivial homomorphism $P_i\to p_j$ is a monomorphism; (c) for every $i,j$ the intersection of any two submodules of $P_j$ isomorphic to $P_i$ contains a submodule isomorphic to $P_i$. Then $\Lambda$ can be represented as a subring associated with a net of ideals in a generalized matrix ring. Bibliography: 5 titles.