In this progress/technical report our objective is twofold. First, to formalize and expand upon remarks appearing in  concerning the relativization of the fundamental identity in the setting of the Brauer group of a ring, and second to exhibit a construction which shows how to interpret uniform distribution as a homological phenomenon.
Gary R. Greenfield. On Uniform and Relative Distribution in the Brauer Group. Technical paper (TR-89-01). Math and Computer Science Technical Report Series. Richmond, Virginia: Department of Mathematics and Computer Science, University of Richmond, March, 1989.