Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassFactorizationAt.map_ne_zero_of_ne_top
∀ {A : Type u_1} [inst : CommRing A] {g : PowerSeries A} {f : Polynomial A} {h : PowerSeries A} {I : Ideal A},
g.IsWeierstrassFactorizationAt f h I → I ≠ ⊤ → (PowerSeries.map (Ideal.Quotient.mk I)) g ≠ 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Top.topstatement and proof · cited by 9,680
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.cast_zeroproof · cited by 1,870
- map_mulproof · cited by 1,137
- Polynomial.mapproof · cited by 806
- PowerSeriesstatement and proof · cited by 797
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassFactorization.map_ne_zeroproof · cited by 3
- PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_topstatement · cited by 2