Theorems · Theorem · commutative algebra
sum_embeddings_eq_finrank_mul
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (F : Type u_6)
[inst_3 : Field F] [inst_4 : Algebra L F] [inst_5 : Algebra K F] [IsScalarTower K L F] (E : Type u_7)
[inst_7 : Field E] [inst_8 : Algebra K E] [IsAlgClosed E] [inst_10 : FiniteDimensional K F] [Algebra.IsSeparable K F]
(pb : PowerBasis K L), ∑ σ, σ ((algebraMap L F) pb.gen) = Module.finrank L F • ∑ σ, σ pb.gen- Defined in
- Mathlib.RingTheory.Trace.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
- Finset.sumstatement and proof · cited by 5,195
- 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.sum_congrproof · cited by 2,323
Cited by1
Results whose statement or proof uses this declaration.
- trace_eq_sum_embeddingsproof · cited by 3