Alternative rings whose associators are not zero-divisors

Erwin Kleinfeld, Yoav Segev

Research output: Contribution to journalArticlepeer-review


The purpose of this short note is to prove that if R is an alternative ring whose associators are not zero-divisors, then R has no zero-divisors. By a result of Bruck and Kleinfeld, if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field.

Original languageEnglish
Pages (from-to)613-616
Number of pages4
JournalArchiv der Mathematik
Issue number6
StatePublished - 1 Dec 2021


  • Alternative ring
  • Associator
  • Commutator
  • Octonion algebra

ASJC Scopus subject areas

  • Mathematics (all)


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