Theorems · Theorem · commutative algebra

AdjoinRoot.Polynomial.quotQuotEquivComm_mk

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (f p : Polynomial R),
  (AdjoinRoot.Polynomial.quotQuotEquivComm I f)
      ((Ideal.Quotient.mk (Ideal.span {Polynomial.map (Ideal.Quotient.mk I) f}))
        (Polynomial.map (Ideal.Quotient.mk I) p)) =
    (Ideal.Quotient.mk (Ideal.span {(Ideal.Quotient.mk (Ideal.map Polynomial.C I)) f}))
      ((Ideal.Quotient.mk (Ideal.map Polynomial.C I)) p)

Defined in

Mathlib.RingTheory.AdjoinRoot

Cited by

1 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRing