Theorems · Theorem · commutative algebra

Polynomial.isIntegral_coeff_of_factors

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Polynomial S),
  IsIntegral R p.leadingCoeff →
    p.Splits → (∀ (x : S), p.IsRoot x → IsIntegral R x) → ∀ (i : ℕ), IsIntegral R (p.coeff i)

Defined in

Mathlib.RingTheory.Polynomial.IsIntegral

Cited by

1 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra