Theorems · Theorem · commutative algebra
MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent
∀ {σ : Type u_1} {R : Type u_2} [inst : TopologicalSpace R] [inst_1 : CommSemiring R] {f : MvPowerSeries σ R},
IsNilpotent (MvPowerSeries.constantCoeff f) → IsTopologicallyNilpotent f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppproof · cited by 5,255
- Filter.atTopproof · cited by 2,405
- MvPowerSeriesstatement and proof · cited by 659
- IsNilpotentstatement and proof · cited by 248
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- Finsupp.degreeproof · cited by 94
- IsTopologicallyNilpotentstatement · cited by 22
- tendsto_atTop_of_eventually_constproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.HasSubst.hasEvalproof · cited by 3