Theorems · Theorem · field theory
Algebra.normalizedTrace_comp_algHom
∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] [inst_3 : CharZero F]
[inst_4 : Algebra.IsIntegral F K] {E : Type u_3} [inst_5 : Field E] [inst_6 : Algebra F E]
[inst_7 : Algebra.IsIntegral F E] (f : E →ₐ[F] K), Algebra.normalizedTrace F K ∘ₗ ↑f = Algebra.normalizedTrace F EThe normalized trace commutes with (injective) maps.
- Defined in
- Mathlib.FieldTheory.NormalizedTrace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- AlgHomstatement and proof · cited by 3,236
- LinearMap.compstatement · cited by 1,642
- CharZerostatement and proof · cited by 932
- LinearMap.extproof · cited by 844
- Algebra.IsIntegralstatement and proof · cited by 224
- SemilinearMapClass.semilinearMapstatement · cited by 80
- Algebra.normalizedTracestatement · cited by 19
- Algebra.normalizedTrace_mapproof · cited by 2
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