In this talk we analyze superrosy division rings, i.e. division rings which admit a well-behaved ordinal valued rank function on definable sets that behaves like a rudimentary notion of dimension. Examples are the quaternions, superstable division rings (which are known to be algebraically closed fields) and more generally supersimple division rings which are commutative. In the talk I shall present superrosyness as a common generalization of o-minimality and supersimplicity and then explain why any superrosy division ring has finite dimension over its center. This is a joint work with Nadja Hempel.
Wed, 11/01/2017 - 22:00 to Thu, 12/01/2017 - 00:00