Number Theory Seminar
Nick Ramsey
DePaul
Euclidean Ideal Classes
Abstract: In the 1970's, Lenstra generalized the notion of a Euclidean ring to that
of a ring with a Euclidean ideal. In the context of Dedekind domains, the
consequence of the existence of such an ideal is the cyclicity of the
class group in much the same way that the consequence of the existence
of a Euclidean algorithm is the triviality of the class group. In this talk,
I'll discuss Lentra's notion in light of some recent developments of Hester Graves.
In particular, I'll discuss a joint result with Graves classifying the quadratic imaginary
fields (which play a rather exception role in the theory) that have a Euclidean ideal.
Wednesday November 4, 2009 at 3:30 PM in SEO 427