  Pfister's Local-Global Principle states that a quadratic form over a
(formally) real field is weakly hyperbolic (i.e. represents a torsion element
in the Witt ring) if and only if its total signature is zero. This result
extends naturally to the setting of central simple algebras with involution.
The present article provides a new proof of this result and extends it to the
case of signatures at preorderings. Furthermore the quantitative relation
between nilpotence and torsion is explored for quadratic forms as well as for
central simple algebras with involution.
