**March 13**

**Chris Conidis**,
CUNY

**The complexity of radical constructions in rings and modules**

We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way. We will spend most of our time describing how to construct radicals that are as complicated as possible from a computability point of view.