Theorems · Theorem · field theory
minpoly.algEquiv_eq
∀ {A : Type u_1} {B : Type u_2} {B' : Type u_3} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Ring B']
[inst_3 : Algebra A B] [inst_4 : Algebra A B'] (f : B ≃ₐ[A] B') (x : B), minpoly A (f x) = minpoly A x- Defined in
- Mathlib.FieldTheory.Minpoly.Basic
- Cited by
- 13 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- AlgEquivstatement and proof · cited by 1,681
- minpolystatement · cited by 439
- AlgEquiv.toAlgHomproof · cited by 273
- AlgEquiv.injectiveproof · cited by 61
- minpoly.algHom_eqproof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- Normal.of_algEquivproof · cited by 4
- AlgEquiv.isSeparable_iffproof · cited by 2
- AlgEquiv.isPurelyInseparableproof · cited by 1
- Normal.minpoly_eq_iff_mem_orbitproof · cited by 1
- PowerBasis.minpolyGen_mapproof · cited by 1
- spectralNorm_eq_of_equivproof · cited by 1
- isConjRoot_of_algEquivproof · cited by 1
- Matrix.minpoly_toLinproof · cited by 0
- LinearMap.minpoly_toMatrixproof · cited by 0
- LinearMap.minpoly_toMatrix'proof · cited by 0
- Matrix.minpoly_toLin'proof · cited by 0
- isConjRoot_of_algEquiv'proof · cited by 0