Supreme Pfister forms

For a nonreal field F of characteristic different from 2, we compare several properties which F may have with respect to an anisotropic n-fold Pfister form π over F. In particular, we consider the situation where the subforms of π are all the anisotropic quadratic forms over F; then π is said to be supreme. We further apply our results to the case where π is the form 2 n × 〈1 〉 (n ≥ 1). In this way we obtain new examples of nonreal fields with prescribed level and with additional properties.