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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… Click to show full abstract
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 ????, the orthogonality graph of the ring Mn(????) of n × n matrices over a skew field ???? is connected and has diameter 4. If n = 2, then the graph of the ring Mn(????) 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.
Keywords:
skew fields;
graphs matrices;
skew field;
orthogonality graphs;
orthogonality;
matrices skew
Journal Title: Journal of Mathematical Sciences
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Mathematical Sciences
Year Published: 2018
Link to full text (if available)
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recommendations!