Net subrings of generalized matrix rings

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.