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Theorems · Theorem · commutative algebra

MvPowerSeries.HasEval.hpow

∀ {σ : Type u_1} {S : Type u_3} [inst : CommRing S] [inst_1 : TopologicalSpace S] {a : σ → S},
  MvPowerSeries.HasEval a → ∀ (s : σ), IsTopologicallyNilpotent (a s)
Defined in
Mathlib.RingTheory.MvPowerSeries.Evaluation
Cited by
6 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
CommRingTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPowerSeries.HasEval.map · cited by 9HasEval.mapPowerSeries.hasEval_iff · cited by 4PowerSeries.hasEval_iffMvPowerSeries.HasEval.mul_left · cited by 4HasEval.mul_leftMvPowerSeries.HasEval.add · cited by 2HasEval.addMvPolynomial.toMvPowerSeries_uniformContinuous · cited by 2MvPolynomial.toMvPowerSer…MvPowerSeries.HasEval.mono · cited by 2HasEval.monoTopologicalSpace · cited by 24529TopologicalSpaceCommRing · cited by 17173CommRingMvPowerSeries.HasEval · cited by 37MvPowerSeries.HasEvalIsTopologicallyNilpotent · cited by 22IsTopologicallyNilpotentHasEval.hpowCITED BYCITES

Cites4

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Cited by6

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