Theorems · Theorem · field theory
IntermediateField.isAlgebraic_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}
{x : ↥S}, IsAlgebraic K x ↔ IsAlgebraic K ↑x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement and proof · cited by 988
- RingHom.injectiveproof · cited by 187
- IsAlgebraicstatement · cited by 163
- isAlgebraic_algebraMap_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
- IntermediateField.isAlgebraic_iSupproof · cited by 1