Theorems · Definition · field theory
Algebra.normalizedTrace
(F : Type u_1) →
(K : Type u_2) →
[inst : Field F] → [inst_1 : Field K] → [inst_2 : Algebra F K] → [CharZero F] → [Algebra.IsIntegral F K] → K →ₗ[F] FThe normalized trace map from an algebraic extension K to the base field F.
- Defined in
- Mathlib.FieldTheory.NormalizedTrace
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- CharZerostatement and proof · cited by 932
- Algebra.IsIntegralstatement and proof · cited by 224
Cited by19
Results whose statement or proof uses this declaration.
- Algebra.normalizedTrace_algebraMap_applystatement · cited by 3
- Algebra.normalizedTrace_algebraMap_apply_eq_selfstatement · cited by 2
- Algebra.normalizedTrace_mapstatement · cited by 2
- Algebra.normalizedTrace_algebraMap_of_liftsstatement · cited by 1
- Algebra.normalizedTrace_defstatement · cited by 1
- Algebra.normalizedTrace_eq_of_finiteDimensional_applystatement · cited by 1
- Algebra.normalizedTrace_minpolystatement · cited by 1
- Algebra.normalizedTrace_selfstatement · cited by 1
- Algebra.normalizedTrace_self_applystatement · cited by 1
- Algebra.normalizedTrace_surjectivestatement · cited by 1
- Algebra.normalizedTrace_trans_applystatement and proof · cited by 1
- Algebra.normalizedTrace_algebraMapstatement · cited by 0