Theorems · Theorem · number theory
FiniteField.algebraMap_norm_eq_pow_sum
∀ (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) = x ^ ∑ i ∈ Finset.range (Module.finrank K L), Nat.card K ^ i
An explicit formula for the norm map: norm[L/K](x) = x ^ (∑ i < [L:K], (#K) ^ i).
- Defined in
- Mathlib.FieldTheory.Finite.Trace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement and proof · cited by 5,195
- Algebra.algebraMapstatement · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Finitestatement and proof · cited by 3,029
- Module.finrankstatement and proof · cited by 1,770
- Finset.rangestatement and proof · cited by 1,341
- Nat.cardstatement and proof · cited by 844
- Algebra.normstatement · cited by 155
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