2021/02/19 by Kleinfeld, Erwin, Segev, Yoav
#FOS: Mathematics #Group Theory (math.GR) #Primary: 17D05 #Rings and Algebras (math.RA) #Secondary: 17A35
paper · doi:10.48550/arxiv.2102.09800
In this paper we prove that if R is a proper alternative ring whose additive group has no 3-torsion and whose non-zero commutators are not zero-divisors, then R has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field. We include other characterizations of octonion division algebras and we also deal with the case where (R,+) has 3-torsion.