Theorems · Theorem · commutative algebra
IsAdjoinRoot.aeval_root_eq_map
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRoot S f), Polynomial.aeval h.root = h.map- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement · cited by 615
- Polynomial.aeval_Xproof · cited by 120
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.rootstatement and proof · cited by 34
- IsAdjoinRoot.mapstatement · cited by 32
- Polynomial.algHom_extproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- IsAdjoinRoot.aeval_root_selfproof · cited by 4
- IsAdjoinRoot.adjoin_root_eq_topproof · cited by 1
- IsAdjoinRoot.lift_self_applyproof · cited by 1
- IsAdjoinRoot.extproof · cited by 1
- IsAdjoinRoot.isAlgebraic_rootproof · cited by 0