Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisorAt.isUnit_shift
∀ {A : Type u_1} [inst : CommRing A] {g : PowerSeries A} {I : Ideal A},
g.IsWeierstrassDivisorAt I →
IsUnit (PowerSeries.mk fun i => (PowerSeries.coeff (i + ((PowerSeries.map (Ideal.Quotient.mk I)) g).order.toNat)) g)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 101 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.
Cites17
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- zero_addproof · cited by 2,366
- HasQuotient.Quotientstatement · cited by 2,301
- IsUnitstatement and proof · cited by 1,602
- PowerSeriesstatement and proof · cited by 797
- Ideal.Quotient.mkstatement and proof · cited by 610
- PowerSeries.coeffstatement and proof · cited by 324
Cited by5
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.coeff_seq_memproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eqproof · cited by 1
- PowerSeries.IsWeierstrassDivisorAt.seq.eq_defstatement and proof · cited by 0
- PowerSeries.IsWeierstrassDivisorAt.seq_onestatement and proof · cited by 0
- PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_memproof · cited by 0