Theorems · Theorem · commutative algebra
MvPolynomial.algHom_C
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {A : Type u_2} [inst_1 : Semiring A] [inst_2 : Algebra R A]
(f : MvPolynomial σ R →ₐ[R] A) (r : R), f (MvPolynomial.C r) = (algebraMap R A) r- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 84 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Cstatement · cited by 400
- AlgHom.commutesproof · cited by 96
Cited by42
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.algebraMap_injectiveproof · cited by 9
- MvPolynomial.bind₁_C_rightproof · cited by 6
- AlgebraicIndependent.restrictScalarsproof · cited by 3
- bind₁_wittPolynomial_xInTermsOfWproof · cited by 3
- MvPolynomial.eval₂_renameproof · cited by 3
- MvPolynomial.exists_rename_eq_of_vars_subset_rangeproof · cited by 3
- AlgebraicIndependent.sumElim_iffproof · cited by 2
- bind₁_xInTermsOfW_wittPolynomialproof · cited by 2
- MvPolynomial.pderiv_renameproof · cited by 2
- MvPolynomial.finSuccEquiv_rename_finSuccEquivproof · cited by 1
- wittPolynomial_zmod_selfproof · cited by 1
- MvPolynomial.universalFactorizationMap_comp_mapproof · cited by 1