The Stacks project

Definition 9.20.1. Let $L/K$ be a finite extension of fields. For $\alpha \in L$ we define the trace $\text{Trace}_{L/K}(\alpha ) = \text{Trace}_ K(\alpha : L \to L)$ and the norm $\text{Norm}_{L/K}(\alpha ) = \det _ K(\alpha : L \to L)$.

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View Definition 9.20.1 as pdf