Theorems · Theorem · commutative algebra

Ring.DirectLimit.Polynomial.exists_of

∀ {ι : Type u_1} [inst : Preorder ι] {G : ι → Type u_2} [inst_1 : (i : ι) → CommRing (G i)]
  {f' : (i j : ι) → i ≤ j → G i →+* G j} [Nonempty ι] [IsDirectedOrder ι]
  (q : Polynomial (Ring.DirectLimit G fun i j h => ⇑(f' i j h))),
  ∃ i p, Polynomial.map (Ring.DirectLimit.of G (fun i j h => ⇑(f' i j h)) i) p = q

Defined in

Mathlib.Algebra.Colimit.Ring

Cited by

0 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderCommRingNonemptyIsDirectedOrder