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Title: Orthogonality Graphs of Matrices Over Skew Fields

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 𝔻, the orthogonality graph of the ring M{sub n}(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 M{sub n}(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.

Authors:
;  [1]
  1. Lomonosov Moscow State University (Russian Federation)
Publication Date:
OSTI Identifier:
22773927
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; FIELD THEORIES; GRAPH THEORY; MATRICES; RINGS

Citation Formats

Guterman, A. E., E-mail: guterman@list.ru, and Markova, O. V., E-mail: ov-markova@mail.ru. Orthogonality Graphs of Matrices Over Skew Fields. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3909-7.
Guterman, A. E., E-mail: guterman@list.ru, & Markova, O. V., E-mail: ov-markova@mail.ru. Orthogonality Graphs of Matrices Over Skew Fields. United States. doi:10.1007/S10958-018-3909-7.
Guterman, A. E., E-mail: guterman@list.ru, and Markova, O. V., E-mail: ov-markova@mail.ru. Wed . "Orthogonality Graphs of Matrices Over Skew Fields". United States. doi:10.1007/S10958-018-3909-7.
@article{osti_22773927,
title = {Orthogonality Graphs of Matrices Over Skew Fields},
author = {Guterman, A. E., E-mail: guterman@list.ru and Markova, O. V., E-mail: ov-markova@mail.ru},
abstractNote = {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 M{sub n}(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 M{sub n}(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.},
doi = {10.1007/S10958-018-3909-7},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 6,
volume = 232,
place = {United States},
year = {2018},
month = {8}
}