Theorems · Theorem · commutative algebra
Polynomial.content_dvd_coeff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p : Polynomial R} (n : ℕ), p.content ∣ p.coeff n- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.supportproof · cited by 237
- NormalizedGCDMonoidstatement and proof · cited by 159
- dvd_zeroproof · cited by 63
- Polynomial.contentstatement and proof · cited by 41
- Polynomial.mem_support_iffproof · cited by 30
- Finset.gcd_dvdproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.dvd_content_iff_C_dvdproof · cited by 3
- Polynomial.content_eq_gcd_range_of_ltproof · cited by 2
- Polynomial.contentIdeal_le_span_contentproof · cited by 1