The Elman-Lam-Krüskemper Theorem

الملخص EN

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.