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Sbornik: Mathematics, 2011, Volume 202, Issue 1, Pages 1–8
DOI: https://doi.org/10.1070/SM2011v202n01ABEH004135 (Mi sm7638) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Ideals of generalized matrix rings

A. V. Budanov

Tomsk State University
English version PDF (212 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2011v202n01ABEH004135
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.
Received: 12.10.2009 and 15.07.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 1, Pages 3–10
DOI: https://doi.org/10.4213/sm7638
Bibliographic databases:
Document Type: Article
UDC: 512.552
MSC: Primary 16S50; Secondary 15A30, 16D20, 16D25
Language: English
Original paper language: Russian
Citation: A. V. Budanov, “Ideals of generalized matrix rings”, Mat. Sb., 202:1 (2011), 3–10; Sb. Math., 202:1 (2011), 1–8
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:669
    Russian version PDF:195
    English version PDF:27
    References:55
    First page:19
     
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