Theorems · Theorem · commutative algebra

Polynomial.isIntegral_coeff_prod

∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (s : Finset ι) (p : ι → Polynomial S),
  (∀ i ∈ s, ∀ (j : ℕ), IsIntegral R ((p i).coeff j)) → ∀ (j : ℕ), IsIntegral R ((s.prod p).coeff j)

Defined in

Mathlib.RingTheory.Polynomial.IsIntegral

Cited by

1 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra