Email this article Orthogonality Graphs of Matrices Over Skew Fields
- Authors: Guterman A.E.1,2, Markova O.V.1,2
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Affiliations:
- Lomonosov Moscow State University
- Moscow Institute of Physics and Technology
- Issue: Vol 232, No 6 (2018)
- Pages: 797-804
- Section: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/241442
- DOI: https://doi.org/10.1007/s10958-018-3909-7
- ID: 241442
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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.
About the authors
A. E. Guterman
Lomonosov Moscow State University; Moscow Institute of Physics and Technology
Author for correspondence.
Email: guterman@list.ru
Russian Federation, Moscow; Dolgoprudny
O. V. Markova
Lomonosov Moscow State University; Moscow Institute of Physics and Technology
Email: guterman@list.ru
Russian Federation, Moscow; Dolgoprudny
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