# The definability of radicals in noncommutative rings

## Chris Conidis

### College of Staten Island - CUNY

We will survey some results in the definability of radicals in rings, focusing on some recent results about noncommutative rings. In particular, we will show that there is no simple definition of the prime radical in the noncommutative setting, thus differentiating prime radicals in commutative/noncommutative rings.

Prof. Conidis received his Ph.D. in mathematics from the University of Chicago in 2009, under the supervision of Denis Hirschfeldt, Antonio Montalban, and Robert Soare, and subsequently held postdoctoral positions at the University of Waterloo and at Vanderbilt University. His work applies techniques of computability theory to problems in algebra, analysis, and combinatorics. He is now an Assistant Professor at the College of Staten Island in CUNY.