Orthogonality Graphs of Matrices Over Skew Fields

A. E. Guterman, O. V. Markova

Research output: Contribution to journalArticlepeer-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 Mn(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 Mn(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 languageEnglish
Pages (from-to)797-804
Number of pages8
JournalJournal of Mathematical Sciences
Volume232
Issue number6
DOIs
StatePublished - 1 Aug 2018
Externally publishedYes

Bibliographical note

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

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