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 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.
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}
}
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4 pages