Theorems · Theorem · field theory
IsAlgebraic.of_aeval
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {r : A} (f : Polynomial R),
f.natDegree ≠ 0 → f.leadingCoeff ∈ nonZeroDivisors R → IsAlgebraic R ((Polynomial.aeval r) f) → IsAlgebraic R r- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- 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
- Submonoidstatement · cited by 3,086
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- nonZeroDivisorsstatement and proof · cited by 895
- Polynomial.aevalstatement and proof · cited by 615
- Polynomial.leadingCoeffstatement and proof · cited by 498
Cited by1
Results whose statement or proof uses this declaration.
- Transcendental.aevalproof · cited by 1