Theorems · Theorem · field theory
IntermediateField.AdjoinSimple.isIntegral_gen
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α : E),
IsIntegral F (IntermediateField.AdjoinSimple.gen F α) ↔ IsIntegral F α- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement · cited by 988
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement and proof · cited by 382
- RingHom.injectiveproof · cited by 187
- IntermediateField.AdjoinSimple.genstatement and proof · cited by 55
- isIntegral_algebraMap_iffproof · cited by 14
- IntermediateField.AdjoinSimple.algebraMap_genproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.norm_eq_norm_adjoinproof · cited by 3