Theorems · Theorem · commutative algebra
Algebra.prod_embeddings_eq_finrank_pow
∀ {K : Type u_4} {L : Type u_5} (F : Type u_6) [inst : Field K] [inst_1 : Field L] [inst_2 : Field F]
[inst_3 : Algebra K L] [inst_4 : Algebra K F] (E : Type u_7) [inst_5 : Field E] [inst_6 : Algebra K E]
[inst_7 : Algebra L F] [IsScalarTower K L F] [IsAlgClosed E] [Algebra.IsSeparable K F]
[inst_11 : FiniteDimensional K F] (pb : PowerBasis K L),
∏ σ, σ ((algebraMap L F) pb.gen) = (∏ σ, σ pb.gen) ^ Module.finrank L F- Defined in
- Mathlib.RingTheory.Norm.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Finset.univstatement and proof · cited by 3,473
- AlgHomstatement and proof · cited by 3,236
- Finset.prodstatement and proof · cited by 2,356
- Finset.cardproof · cited by 2,327
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.norm_eq_prod_embeddingsproof · cited by 5