Theorems · Theorem · field theory
Algebra.normalizedTrace_algebraMap_apply
∀ (F : Type u_3) (E : Type u_4) (K : Type u_5) [inst : Field F] [inst_1 : Field E] [inst_2 : Field K] [inst_3 : Algebra F E] [inst_4 : Algebra E K] [inst_5 : Algebra F K] [IsScalarTower F E K] [inst_7 : Algebra.IsIntegral F E] [inst_8 : Algebra.IsIntegral F K] [inst_9 : CharZero F] (a : E), (Algebra.normalizedTrace F K) ((algebraMap E K) a) = (Algebra.normalizedTrace F E) a
- Defined in
- Mathlib.FieldTheory.NormalizedTrace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- CharZerostatement and proof · cited by 932
- IsScalarTower.toAlgHomproof · cited by 232
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.normalizedTracestatement · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.normalizedTrace_algebraMap_apply_eq_selfproof · cited by 2
- Algebra.normalizedTrace_trans_applyproof · cited by 1
- Algebra.normalizedTrace_algebraMapproof · cited by 0