Theorems · Theorem · commutative algebra
Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPart
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p q : Polynomial R},
q ≠ 0 → (p ∣ q ↔ p.content ∣ q.content ∧ p.primPart ∣ q.primPart)- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
Around this declaration
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Cites17
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_mul_rightproof · cited by 89
- map_dvdproof · cited by 44
- Polynomial.contentstatement and proof · cited by 41
- dvd_mul_of_dvd_leftproof · cited by 25
- mul_dvd_mulproof · cited by 24
- Polynomial.primPartstatement and proof · cited by 19
- Polynomial.eq_C_content_mul_primPartproof · cited by 14
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