Theorems · Theorem · field theory
Polynomial.mapAlg_eq_map
∀ {R : Type u} [inst : CommSemiring R] (S : Type v) [inst_1 : Semiring S] [inst_2 : Algebra R S] (p : Polynomial R),
(Polynomial.mapAlg R S) p = Polynomial.map (algebraMap R S) pmapAlg is the morphism induced by R → S.
- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 111 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.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement · cited by 3,236
- Polynomial.mapstatement · cited by 806
- Polynomial.mapAlgstatement and proof · cited by 13
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.IsSplittingField.IsScalarTower.splitsproof · cited by 2
- Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_Cproof · cited by 2
- Polynomial.coeff_zero_of_isScalarTowerproof · cited by 1
- spectralNorm.spectralMulAlgNorm_eq_of_mem_rootsproof · cited by 1
- spectralNorm.spectralNorm_pow_natDegree_eq_prod_rootsproof · cited by 1
- Polynomial.mapAlg_compproof · cited by 1
- max_norm_root_eq_spectralValueproof · cited by 1
- Polynomial.mem_lifts_iff_mem_algproof · cited by 1
- Polynomial.monic_mapAlg_iffproof · cited by 0