Abstract
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.
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Kleinfeld, E., Segev, Y. Alternative rings whose associators are not zero-divisors. Arch. Math. 117, 613–616 (2021). https://doi.org/10.1007/s00013-021-01646-5
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DOI: https://doi.org/10.1007/s00013-021-01646-5