Geodesic
Ideals of generalized matrix rings
Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 1-8

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Let $R$ and $S$ be rings, and $_RM_S$ and $_SN_R$ bimodules. In the paper, in terms of isomorphisms of lattices, relationships between the lattices of one-sided and two-sided ideals of the generalized matrix ring $K=\bigl(\begin{smallmatrix}R\\N\end{smallmatrix}\bigr)$ and the corresponding lattices of ideals of the rings $R$ and $S$ are described. Necessary and sufficient conditions for a pair of ideals $I$, $J$ of rings $R$ and $S$, respectively, to be the main diagonal of some ideal of the ring $K$ are also obtained. Bibliography: 8 titles.
Keywords: generalized matrix ring, lattice of ideals. 
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     title = {Ideals of generalized matrix rings},
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A. V. Budanov. Ideals of generalized matrix rings. Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/SM_2011_202_1_a0/