Theorems · Theorem · commutative algebra
PowerSeries.isWeierstrassDivision_weierstrassDiv_weierstrassMod
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] (f : PowerSeries A) {g : PowerSeries A},
(PowerSeries.map (IsLocalRing.residue A)) g ≠ 0 →
∀ [inst_2 : IsAdicComplete (IsLocalRing.maximalIdeal A) A], f.IsWeierstrassDivision g (f /ʷ g) (f %ʷ g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialproof · cited by 5,681
- PowerSeriesstatement and proof · cited by 797
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsLocalRing.ResidueFieldstatement · cited by 156
- IsAdicCompletestatement and proof · cited by 124
- PowerSeries.mapstatement and proof · cited by 82
- IsLocalRing.residuestatement and proof · cited by 71
- PowerSeries.IsWeierstrassDivisorAt.divproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivision.uniqueproof · cited by 0