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Zap. Nauchn. Sem. POMI, 2016, Volume 453, Pages 22–32 (Mi znsl6368)  

This article is cited in 1 scientific paper (total in 1 paper)

The lengths of the quaternion and octotion algebras

A. E. Gutermanab, D. K. Kudryavtsevab

a Lomonosov Moscow State University, Moscow, Russia
b Moscow Center for Continuous Mathematical Education, Moscow, Russia

Abstract: The classical Gurvitz theorem claims that there are exactly four normed algebras with division: the real numbers $(\mathbb R)$, complex numbers $(\mathbb C)$, quaternions $(\mathbb H)$, and octonions $(\mathbb O)$. The length of $\mathbb R$ as an algebra over itself is zero; the length of $\mathbb C$ as an $\mathbb R$-algebra equals one. The purpose of the present paper is to prove that the lengths of the $\mathbb R$-algebras of quaternions and octonions equal two and three, respectively.

Key words and phrases: octonions, quaternions, matrix length.

Funding Agency Grant Number
Russian Science Foundation 16-11-10075


Full text: PDF file (183 kB)
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English version:
Journal of Mathematical Sciences (New York), 2017, 224:6, 826–832

Bibliographic databases:

UDC: 512.643+512.552
Received: 14.11.2016

Citation: A. E. Guterman, D. K. Kudryavtsev, “The lengths of the quaternion and octotion algebras”, Computational methods and algorithms. Part XXIX, Zap. Nauchn. Sem. POMI, 453, POMI, St. Petersburg, 2016, 22–32; J. Math. Sci. (N. Y.), 224:6 (2017), 826–832

Citation in format AMSBIB
\Bibitem{GutKud16}
\by A.~E.~Guterman, D.~K.~Kudryavtsev
\paper The lengths of the quaternion and octotion algebras
\inbook Computational methods and algorithms. Part~XXIX
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 453
\pages 22--32
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6368}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3593977}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 6
\pages 826--832
\crossref{https://doi.org/10.1007/s10958-017-3453-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021306363}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. E. Guterman, D. K. Kudryavtsev, O. V. Markova, “Dlina pryamoi summy neassotsiativnykh algebr”, Chislennye metody i voprosy organizatsii vychislenii. XXXII, Zap. nauchn. sem. POMI, 482, POMI, SPb., 2019, 73–86  mathnet
  • Записки научных семинаров ПОМИ
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