Theorems · Theorem · number theory
FiniteField.algebraMap_norm_eq_prod_pow
∀ (K : Type u_1) (L : Type u_2) [inst : Field K] [inst_1 : Field L] [Finite L] [inst_3 : Algebra K L] (x : L), (algebraMap K L) ((Algebra.norm K) x) = ∏ i ∈ Finset.range (Module.finrank K L), x ^ Nat.card K ^ i
An explicit formula for the norm map: norm[L/K](x) = ∏ i < [L:K], x ^ ((#K) ^ i).
- Defined in
- Mathlib.FieldTheory.Finite.Trace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Finset.prodstatement and proof · cited by 2,356
- Module.finrankstatement and proof · cited by 1,770
- AlgEquivproof · cited by 1,681
Cited by1
Results whose statement or proof uses this declaration.
- FiniteField.algebraMap_norm_eq_pow_sumproof · cited by 0