Theorems · Theorem · commutative algebra
AdjoinRoot.algHomOfDvd_root
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (f g : Polynomial S)
(hgf : g ∣ f), (AdjoinRoot.algHomOfDvd R f g hgf) (AdjoinRoot.root f) = AdjoinRoot.root galgHomOfDvd sends AdjoinRoot.root f to AdjoinRoot.root q.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- AdjoinRootstatement · cited by 177
- AdjoinRoot.rootstatement and proof · cited by 77
- AdjoinRoot.algHomOfDvdstatement · cited by 6
- AdjoinRoot.map_rootproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AdjoinRoot.algEquivOfEq_rootproof · cited by 1
- AdjoinRoot.algEquivOfAssociated_rootproof · cited by 0