Theorems · Definition · field theory
IntermediateField.adjoin
(F : Type u_1) →
[inst : Field F] → {E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → Set E → IntermediateField F Eadjoin F S extends a field F by adjoining a set S ⊆ E.
- Cited by
- 382 results in Mathlib
- Foundations
- Depth 77 from the axioms, rests on 1,089 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- IntermediateFieldstatement · cited by 988
- Subfieldproof · cited by 303
- Subring.toSubsemiringproof · cited by 71
- Subfield.closureproof · cited by 39
- Subfield.toSubringproof · cited by 23
Cited by417
Results whose statement or proof uses this declaration.
- IntermediateField.subset_adjoinstatement · cited by 59
- IntermediateField.AdjoinSimple.genstatement · cited by 55
- IntermediateField.adjoin_le_iffstatement and proof · cited by 28
- IntermediateField.adjoin.finiteDimensionalstatement · cited by 21
- IntermediateField.mem_adjoin_simple_selfstatement · cited by 19
- IntermediateField.adjoin.powerBasisstatement · cited by 17
- IntermediateField.FGproof · cited by 17
- IsGalois.card_aut_eq_finrankproof · cited by 16
- IntermediateField.adjoin.finrankstatement · cited by 14
- Field.Emb.Cardinal.leastExtproof · cited by 13
- IsCyclotomicExtension.isGaloisproof · cited by 13
- FiniteGaloisIntermediateField.adjoinproof · cited by 11
Showing the 200 most cited of 417.