Alternative rings whose associators are not zero-divisors
arXiv:2106.11100
Abstract
The purpose of this short note is to prove that if is an alternative ring whose associators are not zero-divisors, then has no zero divisors. By a result of Bruck and Kleinfeld, if, in addition, the characteristic of is not then the central quotient of is an octonion division algebra over some field.
4 pages