A twisted Laurent series ring that is a noncrossed product
Abstract
Description
The striking results on noncrossed products were their existence (Amitsur) and the determination of Q(t) and Q((t)) as their smallest possible centres (Brussel). This paper gives the first fully explicit noncrossed product example over Q((t)). As a consequence, the use of deep number theoretic theorems (local-global principles such as the Hasse norm theorem and density theorems) in order to prove existence is eliminated. Instead, the example can be verified by direct calculations. The noncrossed product proof is short and elementary.
4 pages (A4), updated version of published paper, the sign error in the definition of the element πhas been corrected
4 pages (A4), updated version of published paper, the sign error in the definition of the element πhas been corrected