Theorems · Theorem · commutative algebra

Polynomial.fiberEquivQuotient_tmul

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (f : Polynomial R →ₐ[R] S) (hf : Function.Surjective ⇑f) (p : Ideal R) [inst_3 : p.IsPrime] (a : p.ResidueField)
  (b : Polynomial R),
  (Polynomial.fiberEquivQuotient f hf p) (a ⊗ₜ[R] f b) =
    (Ideal.Quotient.mk (Ideal.map (Polynomial.mapRingHom (algebraMap R p.ResidueField)) (RingHom.ker ↑f)))
      (Polynomial.C a * Polynomial.map (algebraMap R p.ResidueField) b)

Defined in

Mathlib.RingTheory.LocalRing.ResidueField.Polynomial

Cited by

0 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.IsPrime