Quadratic forms over fields of characteristic 2

Abstract

This thesis is concerned with the study of quadratic forms over fields of characteristic 2. First, we consider the extension of quadratic forms to fields of characteristic ≠ 2. Then we make the adjustments necessary to make the characteristic 2 case non-trivial, and investigate the structure of quadratic spaces.

We define equivalence of quadratic forms and investigate a set of invariants. We develop a set of necessary and sufficient conditions for equivalence and give a characterization of non-equivalent forms over certain finite fields.