Theorems · Theorem · field theory
IntermediateField.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}
{x : ↥S}, IsIntegral K x ↔ IsIntegral K ↑x- Cited by
- 3 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.
Cites8
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
- IntermediateFieldstatement and proof · cited by 988
- AlgHom.toRingHomproof · cited by 490
- IsIntegralstatement · cited by 427
- RingHom.injectiveproof · cited by 187
- IntermediateField.valproof · cited by 42
- isIntegral_algHom_iffproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.exists_algHom_adjoin_of_splits_of_aevalproof · cited by 1
- IntermediateField.isAlgebraic_iSupproof · cited by 1
- IntermediateField.exists_finset_of_mem_supr''proof · cited by 0