Abstract:
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
$K=\bigl(\begin{smallmatrix}R&M\\N&S\end{smallmatrix}\bigr)$ 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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