Theorems · Theorem · field theory
minpoly.dvd_iff
∀ {A : Type u_1} {B : Type u_2} [inst : Field A] [inst_1 : Ring B] [inst_2 : Algebra A B] {x : B} {p : Polynomial A},
minpoly A x ∣ p ↔ (Polynomial.aeval x) p = 0- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 121 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.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- MulZeroClass.zero_mulproof · cited by 1,625
- map_mulproof · cited by 1,137
- Polynomial.aevalstatement and proof · cited by 615
- minpolystatement and proof · cited by 439
- minpoly.aevalproof · cited by 91
- minpoly.dvdproof · cited by 31
Cited by4
Results whose statement or proof uses this declaration.
- minpoly.isRadicalproof · cited by 2
- Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_powproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- Algebra.IsUnramifiedAt.not_minpoly_sq_dvdproof · cited by 0