Theorems · Theorem · commutative algebra
trace_eq_sum_automorphisms
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (x : L)
[inst_3 : FiniteDimensional K L] [IsGalois K L], (algebraMap K L) ((Algebra.trace K L) x) = ∑ σ, σ x- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- 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
- Finset.sumstatement and proof · cited by 5,195
- Algebra.algebraMapstatement and proof · cited by 4,706
- Finset.univstatement and proof · cited by 3,473
- AlgHomproof · cited by 3,236
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
Cited by1
Results whose statement or proof uses this declaration.
- FiniteField.algebraMap_trace_eq_sum_powproof · cited by 0