Theorems · Theorem · commutative algebra
Polynomial.IsPrimitive.dvd_primPart_iff_dvd
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p q : Polynomial R},
p.IsPrimitive → q ≠ 0 → (p ∣ q.primPart ↔ p ∣ q)- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- NormalizedGCDMonoidstatement and proof · cited by 159
- Dvd.dvd.transproof · cited by 148
- Associated.symmproof · cited by 87
- Polynomial.contentproof · cited by 41
- Associated.dvdproof · cited by 38
- Polynomial.IsPrimitivestatement and proof · cited by 33
- Dvd.intro_leftproof · cited by 20
- Polynomial.primPartstatement and proof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0
- Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPartproof · cited by 0