Theorems · Theorem · field theory
Polynomial.map_dvd_map
∀ {R : Type u} {S : Type v} [inst : Ring R] [inst_1 : Ring S] (f : R →+* S),
Function.Injective ⇑f → ∀ {x y : Polynomial R}, x.Monic → (Polynomial.map f x ∣ Polynomial.map f y ↔ x ∣ y)- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 122 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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.modByMonicproof · cited by 82
- Polynomial.Monic.mapproof · cited by 52
- Polynomial.map_zeroproof · cited by 33
- Polynomial.map_injectiveproof · cited by 27
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- Polynomial.map_modByMonicproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.map_dvd_map'proof · cited by 14
- minpoly.isIntegrallyClosed_dvdproof · cited by 9
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.eq_rootMultiplicity_mapproof · cited by 1
- IsPrimitiveRoot.minpoly_eq_powproof · cited by 1