Orthogonality Graphs of Matrices Over Skew Fields

A. E. Guterman; O. V. Markova

doi:https://doi.org/10.1007/s10958-018-3909-7

Orthogonality Graphs of Matrices Over Skew Fields

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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 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

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
General Mathematics

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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 {\dh}�”», the orthogonality graph of the ring Mn({\dh}�”») of n × n matrices over a skew field {\dh}�”» is connected and has diameter 4. If n = 2, then the graph of the ring Mn({\dh}�”») 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.",

author = "Guterman, {A. E.} and Markova, {O. V.}",

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AU - Markova, O. V.

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N2 - 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.

AB - 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.

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M3 - مقالة

SN - 1072-3374

VL - 232

SP - 797

EP - 804

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 6

ER -

Orthogonality Graphs of Matrices Over Skew Fields

Abstract

All Science Journal Classification (ASJC) codes

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