English

Alternative rings whose associators are not zero-divisors

Rings and Algebras 2021-06-23 v2 Group Theory

Abstract

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

Keywords

Cite

@article{arxiv.2106.11100,
  title  = {Alternative rings whose associators are not zero-divisors},
  author = {Erwin Kleinfeld and Yoav Segev},
  journal= {arXiv preprint arXiv:2106.11100},
  year   = {2021}
}

Comments

4 pages

R2 v1 2026-06-24T03:25:34.824Z