Theorems · Definition · field theory
Polynomial.mapAlg
(R : Type u) →
[inst : CommSemiring R] →
(S : Type v) → [inst_1 : Semiring S] → [inst_2 : Algebra R S] → Polynomial R →ₐ[R] Polynomial SThe map R[X] → S[X] as an algebra homomorphism.
- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Xproof · cited by 1,639
- Polynomial.aevalproof · cited by 615
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.mapAlg_eq_mapstatement and proof · cited by 9
- Polynomial.IsSplittingField.IsScalarTower.splitsstatement and proof · cited by 2
- Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_Cstatement and proof · cited by 2
- spectralNorm.spectralMulAlgNorm_eq_of_mem_rootsstatement and proof · cited by 1
- spectralNorm.spectralNorm_pow_natDegree_eq_prod_rootsstatement and proof · cited by 1
- Polynomial.mapAlg_compstatement and proof · cited by 1
- Polynomial.monic_of_monic_mapAlgstatement and proof · cited by 1
- Polynomial.coeff_zero_of_isScalarTowerstatement · cited by 1
- max_norm_root_eq_spectralValuestatement and proof · cited by 1
- Polynomial.mem_lifts_iff_mem_algstatement and proof · cited by 1
- spectralNorm.spectralNorm_eq_norm_coeff_zero_rpowproof · cited by 0
- Polynomial.monic_mapAlg_iffstatement · cited by 0