Theorems · Theorem · commutative algebra

AdjoinRoot.map_comp_map

∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  (f : R →+* S) (g : S →+* T) (p : Polynomial R) (q : Polynomial S) (r : Polynomial T) (hf : q ∣ Polynomial.map f p)
  (hg : r ∣ Polynomial.map g q),
  (AdjoinRoot.map g q r hg).comp (AdjoinRoot.map f p q hf) = AdjoinRoot.map (g.comp f) p r ⋯

Defined in

Mathlib.RingTheory.AdjoinRoot

Cited by

0 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRing