The lengths of the quaternion and octonion algebras

A. E. Guterman; D. K. Kudryavtsev

doi:10.1007/s10958-017-3453-x

The lengths of the quaternion and octonion algebras

A. E. Guterman, D. K. Kudryavtsev

Lomonosov Moscow State University

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

8 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	826-832
Number of pages	7
Journal	Journal of Mathematical Sciences
Volume	224
Issue number	6
DOIs	https://doi.org/10.1007/s10958-017-3453-x
State	Published - Aug 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 Springer Science+Business Media New York.

Funding

This work was supported by the Russian Science Foundation (project No. 16-11-10075).

Funders	Funder number
Russian Science Foundation	16-11-10075

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10.1007/s10958-017-3453-x

Cite this

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The lengths of the quaternion and octonion algebras

Abstract

Bibliographical note

Funding

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