Orthogonality Graphs of Matrices Over Skew Fields

The paper is devoted to studying the orthogonality graph of the matrix ring over a skew field. It is shown that for n ≥ 3 and an arbitrary skew field 𝔻, the orthogonality graph of the ring M n (𝔻) of n × n matrices over a skew field 𝔻 is connected and has diameter 4. If n = 2, then the graph of the...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 232; no. 6; pp. 797 - 804
Main Authors Guterman, A. E., Markova, O. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 02.08.2018
Springer
Springer Nature B.V
Subjects
FIELD THEORIES
GRAPH THEORY
Graphs
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
MATRICES
Orthogonality
RINGS
Rings (mathematics)
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Summary:The paper is devoted to studying the orthogonality graph of the matrix ring over a skew field. It is shown that for n ≥ 3 and an arbitrary skew field 𝔻, the orthogonality graph of the ring M n (𝔻) of n × n matrices over a skew field 𝔻 is connected and has diameter 4. If n = 2, then the graph of the ring M n (𝔻) is a disjoint union of connected components of diameters 1 and 2. As a corollary, the corresponding results on the orthogonality graphs of simple Artinian rings are obtained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3909-7