Theorems · Theorem · commutative algebra
PowerSeries.coeff_mul_mem_ideal_of_coeff_left_mem_ideal
∀ {A : Type u_1} [inst : Semiring A] {I : Ideal A} {f g : PowerSeries A} (n : ℕ) [I.IsTwoSided],
(∀ i ≤ n, (PowerSeries.coeff i) f ∈ I) → ∀ i ≤ n, (PowerSeries.coeff i) (f * g) ∈ I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement and proof · cited by 324
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.one_eq_topproof · cited by 83
- PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_idealproof · cited by 4
- Ideal.IsTwoSided.mul_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_memproof · cited by 1