Theorems · Theorem · commutative algebra
Algebra.norm_eq_prod_automorphisms
∀ {L : Type u_6} (K : Type u_7) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
[inst_3 : FiniteDimensional K L] [IsGalois K L] (x : L), (algebraMap K L) ((Algebra.norm K) x) = ∏ σ, σ x- Defined in
- Mathlib.RingTheory.Norm.Transitivity
- Cited by
- 5 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.
Cites21
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Finset.univstatement and proof · cited by 3,473
- AlgHomproof · cited by 3,236
- Finset.prodstatement and proof · cited by 2,356
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
Cited by5
Results whose statement or proof uses this declaration.
- prod_galRestrict_eq_normproof · cited by 1
- groupCohomology.norm_ofAlgebraAutOnUnits_eqproof · cited by 1
- FiniteField.algebraMap_norm_eq_powproof · cited by 1
- FiniteField.algebraMap_norm_eq_prod_powproof · cited by 1
- RingOfIntegers.dvd_normproof · cited by 1