Number theory deals with properties of the integers, rings of algebraic integers, and a variety of arithmetic objects such as elliptic curves. Many crowning achievements of the human intellect can be found in this beautiful branch of mathematics, with the tradition dating back to the ancient Greeks. The number theory community in the Pure Mathematics department at the University of Waterloo includes seven regular faculty members:
- Jan. 22, 2019
Daniel Smertnig, Department of Pure Mathematics, University of Waterloo
Quaternion orders can possess many different ring-theoretical properties, such as being maximal, hereditary, Eichler, Bass, or Gorenstein. I will recall these properties and their relations to each other, summarizing a 'taxonomy' of quaternion orders. A quaternion order O over a domain R is basic if it contains an integrally closed quadratic R-order. I will show that a quaternion order is Bass if and only if it is basic, in the local and global settings.