The Elman-Lam-Krüskemper Theorem

For a (formally) real field , the vanishing of a certain power of the fundamental ideal in the Witt ring of √(−1) implies that the same power of the fundamental ideal in the Witt ring of 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 . This fact is very difficult to prove in general, but has an elementary proof under an assumption on the stability index of . We present an exposition of these results.