Derivation algebras of finitely generated Witt rings (Q1073841)

We consider derivations of an abstract, finitely generated Witt ring R. Denote the collection of derivations by Der(R); it is a Lie algebra under the usual bracket operation. The structure of Der(R) is closely related to the structure of the torsion part of R, which is the part least understood. A lengthy computation yields Der(R) for Witt rings of elementary type. We then show Der(R) is a simple Lie algebra iff R is a group ring extension of \({\mathbb{Z}}/2{\mathbb{Z}}\). We also classify the Witt rings R such that \(Der(R)=0\) or Der(R) contains a non-integrable derivation.