Theorems · Theorem · field theory
IsSeparable.tower_bot
∀ {F : Type u_1} [inst : Field F] {K : Type u_2} {E : Type u_3} [inst_1 : Field K] [inst_2 : Ring E]
[inst_3 : Algebra F K] [inst_4 : Algebra F E] [inst_5 : Algebra K E] [Nontrivial E] [IsScalarTower F K E] {x : K},
IsSeparable F ((algebraMap K E) x) → IsSeparable F xIf E / K / F is a scalar tower and algebraMap K E x is separable over F, then x is
also separable over F.
- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialstatement and proof · cited by 2,416
- minpolyproof · cited by 439
- Polynomial.Separableproof · cited by 117
- minpoly.aevalproof · cited by 91
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.isSeparable_tower_bot_of_isSeparableproof · cited by 5
- IsSeparable.of_algHomproof · cited by 1