3 papers
math.RA2021
A uniform characterization of the octonions and the quaternions using commutators
Erwin Kleinfeld, Yoav Segev
Let be a ring with which is not commutative. Assume that a non-zero commutator in is not a zero divisor. Assume further that either is alternative, but not as…
math.RA2021
Alternative rings whose associators are not zero-divisors
Erwin Kleinfeld, Yoav Segev
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 Klein…
math.RA2021
A short characterization of the Octonions
Erwin Kleinfeld, Yoav Segev
In this paper we prove that if is a proper alternative ring whose additive group has no -torsion and whose non-zero commutators are not zero-divisors, then has no zero-d…