Theorems · Definition · commutative algebra

Polynomial.IsDistinguishedAt.algEquivQuotient

{A : Type u_1} →
  [inst : CommRing A] →
    {g : Polynomial A} →
      {I : Ideal A} →
        g.IsDistinguishedAt I →
          [IsAdicComplete I A] → (Polynomial A ⧸ Ideal.span {g}) ≃ₐ[A] PowerSeries A ⧸ Ideal.span {↑g}

A distinguished polynomial g induces a natural isomorphism A[X] / (g) ≃ₐ[A] A⟦X⟧ / (g).

Defined in

Mathlib.RingTheory.PowerSeries.WeierstrassPreparation

Cited by

4 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsAdicComplete