2021/07/21 by Kleinfeld, Erwin, Segev, Yoav
#FOS: Mathematics #Primary: 12E15 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2107.09933
Let R be an associative ring with \bf 1 which is not commutative. Assume that any non-zero commutator v∈ R satisfies: v2 is in the center of R and v is not a zero-divisor. (Note that our assumptions do not include finite dimensionality.) We prove that R has no zero divisors, and that if \rm char(R)≠ 2, then the localization of R at its center is a quaternion division algebra.