Theorems · Theorem · field theory
Polynomial.map_dvd
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) {x y : Polynomial R},
x ∣ y → Polynomial.map f x ∣ Polynomial.map f y- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.mapRingHomproof · cited by 98
- map_dvdproof · cited by 44
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.natSepDegree_le_of_dvdproof · cited by 3
- Ideal.IsFractionRing.normalproof · cited by 3
- Polynomial.count_map_rootsproof · cited by 2
- Polynomial.cyclotomic.dvd_X_pow_sub_oneproof · cited by 2
- Field.finite_intermediateField_of_exists_primitive_elementproof · cited by 1
- Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_Xproof · cited by 1
- integralClosure.mem_lifts_of_monic_of_dvd_mapproof · cited by 1
- Polynomial.cyclotomic_dvd_geom_sum_of_dvdproof · cited by 0
- Polynomial.coeff_mem_radical_span_coeff_of_dvdproof · cited by 0