Theorems · Definition · field theory
Polynomial.MonicDegreeEq.map
{R : Type u} →
{S : Type v} →
{n : ℕ} →
[inst : Semiring R] →
[inst_1 : Semiring S] → Polynomial.MonicDegreeEq R n → (R →+* S) → Polynomial.MonicDegreeEq S nThe image of a monic polynomial of degree n under a ring homomorphism.
- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Polynomial.mapproof · cited by 806
- Polynomial.MonicDegreeEqstatement and proof · cited by 22
Cited by16
Results whose statement or proof uses this declaration.
- MvPolynomial.mapEquivMonicproof · cited by 10
- Polynomial.MonicDegreeEq.map_coestatement and proof · cited by 6
- Polynomial.UniversalCoprimeFactorizationRing.factor₁proof · cited by 4
- Polynomial.UniversalCoprimeFactorizationRing.factor₂proof · cited by 4
- MvPolynomial.pderiv_inl_universalFactorizationMap_Xproof · cited by 1
- MvPolynomial.pderiv_inr_universalFactorizationMap_Xproof · cited by 1
- MvPolynomial.mapEquivMonic_symm_mapstatement and proof · cited by 1
- Polynomial.UniversalCoprimeFactorizationRing.exists_liesOver_residueFieldMap_bijectivestatement and proof · cited by 1
- Polynomial.UniversalCoprimeFactorizationRing.factor₁_mul_factor₂statement · cited by 1
- Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fststatement and proof · cited by 1
- Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_sndstatement and proof · cited by 1
- Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂proof · cited by 1