Theorems · Theorem · field theory
Algebra.IsSeparable.isSeparable
∀ (F : Type u_1) {K : Type u_3} [inst : CommRing F] [inst_1 : Ring K] [inst_2 : Algebra F K] [Algebra.IsSeparable F K]
(x : K), IsSeparable F x- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebra.IsSeparablestatement and proof · cited by 210
- IsSeparablestatement · cited by 68
- Algebra.IsSeparable.isSeparable'proof · cited by 2
Cited by30
Results whose statement or proof uses this declaration.
- Algebra.IsSeparable.isIntegralproof · cited by 8
- IntermediateField.isSeparable_of_mem_isSeparableproof · cited by 7
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- IsPurelyInseparable.surjective_algebraMap_of_isSeparableproof · cited by 6
- Algebra.IsSeparable.of_equiv_equivproof · cited by 6
- separableClosure.eq_top_iffproof · cited by 6
- Algebra.norm_eq_prod_embeddingsproof · cited by 5
- Algebra.FormallyUnramified.of_isSeparableproof · cited by 5
- Algebra.isSeparable_tower_bot_of_isSeparableproof · cited by 5
- Algebra.isSeparable_tower_top_of_isSeparableproof · cited by 4
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- AlgEquiv.Algebra.isSeparableproof · cited by 3