Table of Contents
ISRN Algebra
Volume 2011 (2011), Article ID 106823, 8 pages
http://dx.doi.org/10.5402/2011/106823
Research Article

The Elman-Lam-Krüskemper Theorem

1Universität Konstanz, Zukunftskolleg/FB Mathematik und Statistik, 78457 Konstanz, Germany
2Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA

Received 10 May 2011; Accepted 1 June 2011

Academic Editors: D. Herbera and H. You

Copyright © 2011 Karim Johannes Becher and David B. Leep. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a (formally) real field 𝐾, the vanishing of a certain power of the fundamental ideal in the Witt ring of 𝐾(1) implies that the same power of the fundamental ideal in the Witt ring of 𝐾 is torsion free. The proof of this statement involves a fact on the structure of the torsion part of powers of the fundamental ideal in the Witt ring of 𝐾. This fact is very difficult to prove in general, but has an elementary proof under an assumption on the stability index of 𝐾. We present an exposition of these results.