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math.RA2018
The finiteness of the genus of a finite-dimensional division algebra, and some generalizations
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applic…
math.RA2013
The genus of a division algebra and the unramified Brauer group
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
Let D be a finite-dimensional central division algebra over a field K. We define the genus gen(D) of D to be the collection of classes in the Brauer group of K represented by centr…