Theorems · Theorem · field theory
IntermediateField.coe_isIntegral_iff
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {S : IntermediateField K L}
{R : Type u_3} [inst_3 : CommRing R] [inst_4 : Algebra R K] [inst_5 : Algebra R L] [inst_6 : IsScalarTower R K L]
{x : ↥S}, IsIntegral R ↑x ↔ IsIntegral R x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- IntermediateFieldstatement and proof · cited by 988
- IsIntegralstatement · cited by 427
- Subtype.val_injectiveproof · cited by 232
- AlgHom.restrictScalarsproof · cited by 83
- IntermediateField.valproof · cited by 42
- isIntegral_algHom_iffproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.pow_eq_one_of_mahlerMeasure_eq_oneproof · cited by 1