Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassFactorization.map_ne_zero
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] {g : PowerSeries A} {f : Polynomial A}
{h : PowerSeries A}, g.IsWeierstrassFactorization f h → (PowerSeries.map (IsLocalRing.residue A)) g ≠ 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- PowerSeriesstatement and proof · cited by 797
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.ResidueFieldstatement · cited by 156
- PowerSeries.mapstatement · cited by 82
- IsLocalRing.residuestatement · cited by 71
- Ideal.IsMaximal.ne_topproof · cited by 42
- PowerSeries.IsWeierstrassFactorizationstatement and proof · cited by 13
- PowerSeries.IsWeierstrassFactorizationAt.map_ne_zero_of_ne_topproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassFactorization.elimproof · cited by 5
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionproof · cited by 1
- PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_mapstatement · cited by 1