Theorems · Definition · commutative algebra

PowerSeries.weierstrassDistinguished

{A : Type u_1} →
  [inst : CommRing A] →
    [inst_1 : IsLocalRing A] →
      [IsAdicComplete (IsLocalRing.maximalIdeal A) A] →
        (g : PowerSeries A) → (PowerSeries.map (IsLocalRing.residue A)) g ≠ 0 → Polynomial A

The f in the Weierstrass preparation theorem.

Defined in

Mathlib.RingTheory.PowerSeries.WeierstrassPreparation

Cited by

8 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsLocalRingIsAdicComplete