A short characterization of the octonions

Erwin Kleinfeld, Yoav Segev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article, we prove that if R is a proper alternative ring whose additive group has no 3-torsion and whose non-zero commutators are not zero-divisors, then R has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field. We include other characterizations of octonion division algebras and we also deal with the case where (Formula presented.) has 3-torsion.

Original languageEnglish
Pages (from-to)5347-5353
Number of pages7
JournalCommunications in Algebra
Volume49
Issue number12
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Alternative ring
  • associator
  • commutator
  • octonion algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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