Field norm

Let $𝐿 : 𝐾$ be a field extension of finite degree $𝑛$ , and identify $𝐿$ with $𝐾 𝑛$ For any $𝛾 \in 𝐾$ let $Λ (𝛾)$ denote the left-multiplication operator. The field norm $𝑁 𝐿 : 𝐾 (𝛾)$ is defined as the Determinant of $Λ (𝛾)$ ring

𝑁 𝐿 : 𝐾 : 𝐿 \to 𝐾 𝛾 \mapsto d e t Λ (𝛾)

Special cases

Norm of a number field

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Field norm

Special cases

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