Theorems · Theorem · field theory
isConjRoot_of_algEquiv
∀ {R : Type u_1} {A : Type u_5} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (x : A) (s : A ≃ₐ[R] A),
IsConjRoot R x (s x)Let s be an R-algebra isomorphism. Then s x is a conjugate root of x.
- Defined in
- Mathlib.FieldTheory.Minpoly.IsConjRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AlgEquivstatement and proof · cited by 1,681
- IsConjRootstatement · cited by 43
- minpoly.algEquiv_eqproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- isConjRoot_iff_exists_algEquivproof · cited by 2