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

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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. 
@article{ZNSL_1994_211_a16,
     author = {A. V. Yakovlev},
     title = {Net subrings of generalized matrix rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--198},
     publisher = {mathdoc},
     volume = {211},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a16/}
}
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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/