Theorems · Definition · field theory
IntermediateField.adjoinRootEquivAdjoin
(F : Type u_1) →
[inst : Field F] →
{E : Type u_2} →
[inst_1 : Field E] → [inst_2 : Algebra F E] → {α : E} → IsIntegral F α → AdjoinRoot (minpoly F α) ≃ₐ[F] ↥F⟮α⟯algebra isomorphism between AdjoinRoot and F⟮α⟯
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement · cited by 1,681
- IntermediateFieldstatement · cited by 988
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement and proof · cited by 382
- AdjoinRootstatement · cited by 177
- Algebra.ofIdproof · cited by 166
- IntermediateField.AdjoinSimple.genproof · cited by 55
- AlgEquiv.ofBijectiveproof · cited by 34
Cited by8
Results whose statement or proof uses this declaration.
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- minpoly.algEquivproof · cited by 2
- IntermediateField.adjoinRootEquivAdjoin_apply_rootstatement · cited by 2
- Differential.differentialFiniteDimensionalproof · cited by 1
- minpoly.algEquiv_applyproof · cited by 1
- IntermediateField.adjoinRootEquivAdjoin_symm_apply_genstatement and proof · cited by 1
- Differential.differentialAlgebraFiniteDimensionalproof · cited by 0
- IntermediateField.powerBasisAuxproof · cited by 0