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Tag 0BIK

Chapter 9: Fields > Section 9.20: Trace and norm

Definition 9.20.6. Let $L/K$ be a finite extension of fields. The trace pairing for $L/K$ is the symmetric $K$-bilinear form $$ Q_{L/K} : L \times L \longrightarrow K,\quad (\alpha, \beta) \longmapsto \text{Trace}_{L/K}(\alpha\beta) $$

    The code snippet corresponding to this tag is a part of the file fields.tex and is located in lines 2408–2416 (see updates for more information).

    \begin{definition}
    \label{definition-trace-pairing}
    Let $L/K$ be a finite extension of fields. The {\it trace pairing}
    for $L/K$ is the symmetric $K$-bilinear form
    $$
    Q_{L/K} : L \times L \longrightarrow K,\quad
    (\alpha, \beta) \longmapsto \text{Trace}_{L/K}(\alpha\beta)
    $$
    \end{definition}

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