A CHARACTERISATION OF THE QUATERNIONS USING COMMUTATORS

Erwin Kleinfeld; Yoav Segev

doi:10.1353/mpr.2022.0000

A CHARACTERISATION OF THE QUATERNIONS USING COMMUTATORS

Erwin Kleinfeld, Yoav Segev

Department of Mathematics

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

1 Scopus citations

Abstract

Let R be an associative ring with 1, which is not commutative. Assume that any non-zero commutator v ∈ R satisfies: v² is in the centre of R, and v is not a zero divisor. We prove that R has no zero divisors, and that if char(R) ≠ 2, then the localisation of R at its centre is a quaternion division algebra. Our proof is elementary and self contained.

Original language	English
Pages (from-to)	1-4
Number of pages	4
Journal	The Mathematical Proceedings of the Royal Irish Academy
Volume	122A
Issue number	1
DOIs	https://doi.org/10.1353/mpr.2022.0000
State	Published - 1 Jan 2022

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Algebra and Number Theory
Applied Mathematics

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abstract = "Let R be an associative ring with 1, which is not commutative. Assume that any non-zero commutator v ∈ R satisfies: v2 is in the centre of R, and v is not a zero divisor. We prove that R has no zero divisors, and that if char(R) ≠ 2, then the localisation of R at its centre is a quaternion division algebra. Our proof is elementary and self contained.",

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A CHARACTERISATION OF THE QUATERNIONS USING COMMUTATORS

Abstract

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