Theorems · Theorem · commutative algebra

MvPowerSeries.IsNilpotent_substAlgHom

∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] {τ : Type u_4} {S : Type u_5} [inst_1 : CommRing S]
  [inst_2 : Algebra R S] {a : σ → MvPowerSeries τ S} (ha : MvPowerSeries.HasSubst a) {f : MvPowerSeries σ R},
  IsNilpotent (MvPowerSeries.constantCoeff f) →
    IsNilpotent (MvPowerSeries.constantCoeff ((MvPowerSeries.substAlgHom ha) f))

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

2 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra