The lengths of the quaternion and octonion algebras

A. E. Guterman, D. K. Kudryavtsev

Research output: Contribution to journalArticlepeer-review

5 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 languageEnglish
Pages (from-to)826-832
Number of pages7
JournalJournal of Mathematical Sciences
Volume224
Issue number6
DOIs
StatePublished - Aug 2017
Externally publishedYes

Bibliographical note

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

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