Theorems · Theorem · commutative algebra
IsIntegral.of_aeval_monic
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {x : A}
{p : Polynomial R}, p.Monic → p.natDegree ≠ 0 → IsIntegral R ((Polynomial.aeval x) p) → IsIntegral R x- Cited by
- 1 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.
Cites15
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
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.aevalstatement and proof · cited by 615
- Polynomial.Monicstatement and proof · cited by 461
- IsIntegralstatement and proof · cited by 427
- Polynomial.eval₂proof · cited by 267
- Polynomial.compproof · cited by 193
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegral.of_aeval_monic_of_isIntegral_coeffproof · cited by 1