Theorems · Theorem · commutative algebra

IsAdjoinRoot.apply_eq_lift

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
  (h : IsAdjoinRoot S f) {T : Type u_1} [inst_3 : CommRing T] {i : R →+* T} {x : T} (hx : Polynomial.eval₂ i x f = 0)
  (g : S →+* T), (∀ (a : R), g ((algebraMap R S) a) = i a) → g h.root = x → ∀ (a : S), g a = (h.lift i x hx) a

Auxiliary lemma for apply_eq_lift

Defined in

Mathlib.RingTheory.IsAdjoinRoot

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingRingAlgebraCommRing