Theorems · Theorem · commutative algebra
Polynomial.dvd_content_iff_C_dvd
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p : Polynomial R} {r : R},
r ∣ p.content ↔ Polynomial.C r ∣ p- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- Polynomial.supportproof · cited by 237
- NormalizedGCDMonoidstatement and proof · cited by 159
- Dvd.dvd.transproof · cited by 148
- Polynomial.contentstatement and proof · cited by 41
- Finset.dvd_gcd_iffproof · cited by 9
- Polynomial.content_dvd_coeffproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.IsPrimitive.mul_map_mem_lifts_iffproof · cited by 2
- Polynomial.C_content_dvdproof · cited by 1
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0