Theorems · Theorem · field theory
Algebra.isSeparable_iff
∀ {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), IsIntegral F x ∧ IsSeparable F x- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 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
- IsIntegralstatement and proof · cited by 427
- Algebra.IsSeparablestatement and proof · cited by 210
- IsSeparablestatement and proof · cited by 68
- Algebra.IsSeparable.isSeparableproof · cited by 30
- Algebra.IsSeparable.isIntegralproof · cited by 8
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