Theorems · Theorem · commutative algebra
Algebra.Generators.ofComp_toAlgHom_monomial_sumElim
∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
{ι' : Type u_3} {T : Type u_7} [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
[inst_6 : IsScalarTower R S T] (Q : Algebra.Generators S T ι') (P : Algebra.Generators R S ι) (v₁ : ι' →₀ ℕ)
(v₂ : ι →₀ ℕ) (a : R),
(Q.ofComp P).toAlgHom ((MvPolynomial.monomial (v₁.sumElim v₂)) a) =
(MvPolynomial.monomial v₁) ((MvPolynomial.aeval P.val) ((MvPolynomial.monomial v₂) a))- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- mul_commproof · cited by 2,262
- MvPolynomialstatement and proof · cited by 2,140
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Generators.map_toComp_kerproof · cited by 3