## 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 pairingfor $L/K$ 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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