Theorems · Theorem · commutative algebra
Polynomial.content_eq_zero_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p : Polynomial R}, p.content = 0 ↔ p = 0- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 83 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.
Cites8
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.coeffproof · cited by 1,045
- Polynomial.supportproof · cited by 237
- NormalizedGCDMonoidstatement and proof · cited by 159
- Polynomial.extproof · cited by 118
- Polynomial.contentstatement · cited by 41
- Finset.gcd_eq_zero_iffproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.isPrimitive_primPartproof · cited by 4
- Polynomial.natDegree_primPartproof · cited by 2
- Polynomial.associated_primPart_mulproof · cited by 2
- Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPartproof · cited by 1
- Polynomial.eval₂_primPart_eq_zeroproof · cited by 0
- Polynomial.aeval_primPart_eq_zeroproof · cited by 0
- Polynomial.primPart_mulproof · cited by 0