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Theorems · Definition · commutative algebra

AdjoinRoot.algHomOfDvd

(R : Type u_1) →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] → [inst_2 : Algebra R S] → (f g : Polynomial S) → g ∣ f → AdjoinRoot f →ₐ[R] AdjoinRoot g

The canonical algebraic homomorphism from AdjoinRoot f to AdjoinRoot g, where the polynomial g : S[X] divides f.

Defined in
Mathlib.RingTheory.AdjoinRoot
Cited by
6 results in Mathlib
Foundations
Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AdjoinRoot.algHomOfDvd_root · cited by 2AdjoinRoot.algHomOfDvd_ro…AdjoinRoot.coe_algEquivOfAssociated · cited by 1AdjoinRoot.coe_algEquivOf…AdjoinRoot.coe_algEquivOfEq · cited by 1AdjoinRoot.coe_algEquivOf…AdjoinRoot.algEquivOfAssociated_toAlgHom · cited by 0AdjoinRoot.algEquivOfAsso…AdjoinRoot.coe_algHomOfDvd · cited by 0AdjoinRoot.coe_algHomOfDvdAdjoinRoot.algEquivOfEq_toAlgHom · cited by 0AdjoinRoot.algEquivOfEq_t…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraPolynomial · cited by 5681PolynomialAlgHom · cited by 3236AlgHomAlgHom.id · cited by 196AlgHom.idAdjoinRoot · cited by 177AdjoinRootAdjoinRoot.mapAlgHom · cited by 6AdjoinRoot.mapAlgHomAdjoinRoot.algHomOfDvdCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.