University of Georgia
Mathematics Department Colloquium
Professor Arpad Toth
Fordham University
October 5, 2000
Factorization of primes in rings of algebraic integers
Abstract: Given a polynomial with rational
coefficients one can use a root of the polynomial to construct a
finite ring extension of the ring of ordinary integers. A fundamental
arithmetic problem is to determine, how ordinary prime numbers factor
in this extension. (Many times they do!) In the first half of the talk
I will illustrate through examples how this problem is solved in case
the Galois group of the equation is abelian. At the end I plan to
outline a solution to the problem in a non-abelian situation using
Felix Klein's solution of the quintic equation. (This is joint work
with W. Duke.)