Theorems · Theorem · field theory
Algebra.isSeparable_tower_top_of_isSeparable
∀ (F : Type u_1) (L : Type u_2) [inst : CommRing F] (E : Type u_4) [inst_1 : Field L] [inst_2 : Ring E] [inst_3 : Algebra F L] [inst_4 : Algebra F E] [inst_5 : Algebra L E] [IsScalarTower F L E] [Algebra.IsSeparable F E], Algebra.IsSeparable L E
If E / K / F is an extension tower, E is separable over F, then it's also separable
over K.
- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- Algebra.IsSeparablestatement and proof · cited by 210
- Algebra.IsSeparable.isSeparableproof · cited by 30
- IsSeparable.tower_topproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- differentIdeal_eq_differentIdeal_mul_differentIdealproof · cited by 3
- separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparableproof · cited by 2
- sum_embeddings_eq_finrank_mulproof · cited by 1
- Algebra.prod_embeddings_eq_finrank_powproof · cited by 1