Theorems · Theorem · commutative algebra
Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
∀ {R : Type u} [inst : CommRing R] {𝓟 : Ideal R} {f : Polynomial R},
f.IsWeaklyEisensteinAt 𝓟 → ∀ {x : R}, f.IsRoot x → f.Monic → ∀ (i : ℕ), f.natDegree ≤ i → x ^ i ∈ 𝓟- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Idealstatement and proof · cited by 4,748
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.Monicstatement and proof · cited by 461
- pow_addproof · cited by 315
- Finset.sum_insertproof · cited by 196
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroproof · cited by 1