Orthogonality Graphs of Matrices Over Skew Fields

A. E. Guterman; O. V. Markova

doi:10.1007/s10958-018-3909-7

Orthogonality Graphs of Matrices Over Skew Fields

A. E. Guterman, O. V. Markova

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 ð�”», the orthogonality graph of the ring M_n(ð�”») of n × n matrices over a skew field ð�”» is connected and has diameter 4. If n = 2, then the graph of the ring M_n(ð�”») 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.

Original language	English
Pages (from-to)	797-804
Number of pages	8
Journal	Journal of Mathematical Sciences
Volume	232
Issue number	6
DOIs	https://doi.org/10.1007/s10958-018-3909-7
State	Published - 1 Aug 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

This work was supported by the Russian Science Foundation (grant No. 17-11-01124).

Funders	Funder number
Russian Science Foundation	17-11-01124

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10.1007/s10958-018-3909-7

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Orthogonality Graphs of Matrices Over Skew Fields

Abstract

Bibliographical note

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