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 Mn(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 Mn(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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 81–93.
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Guterman, A.E., Markova, O.V. Orthogonality Graphs of Matrices Over Skew Fields. J Math Sci 232, 797–804 (2018). https://doi.org/10.1007/s10958-018-3909-7
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DOI: https://doi.org/10.1007/s10958-018-3909-7