MATHEMATICS COLLOQUIUM

 WHEN:
On Thursday, February 24, 2000 at 2:20 PM

WHERE:
Durham Science Center, Room 255

WHAT:

Griff Elder
Department of Mathematics
University of Nebraska at Omaha

will give a talk on

Galois Action in Biquadratic Extensions

Abstract:
The Normal Basis Theorem, a basic result in Algebra, says that Galois Field Extensions and Group Algebras are essentially the same. If N/K is a finite Galois extension of number fields, then N is ``isomorphic'' to K[G], where G is the Galois group. More precisely, it says that N is free over K[G].

    Are Galois Ring Extensions and Group Rings essentially the same?

    Is the ring of integers of N free over the group ring Z[G], where Z is the set of rational integers? Interestingly enough, as E. Noether noted, the answer depends upon prime decomposition.

The question was recently solved for biquadratic extensions. While this new result will be the primary focus of the talk, it will be proceeded by a brief description the status of this question, and some developments over the past 30 years, in particular results in Integral Representation Theory.