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doc(ring_theory/norm) norm_eq_prod_embeddings docstring (#10242)
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Co-authored-by: Chris Birkbeck <56166236+CBirkbeck@users.noreply.github.com>
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CBirkbeck and CBirkbeck committed Nov 10, 2021
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variable (K)

/-- For `L/K` a finite separable extension of fields and `E` an algebraically closed extension
of `K`, the norm (down to `K`) of an element `x` of `L` is equal to the product of the images
of `x` over all the `K`-embeddings `σ` of `L` into `E`. -/
lemma norm_eq_prod_embeddings [finite_dimensional K L] [is_separable K L] [is_alg_closed E]
{x : L} : algebra_map K E (norm K x) = ∏ σ : L →ₐ[K] E, σ x :=
begin
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