Theorems · Theorem · commutative algebra
Polynomial.IsPrimitive.ne_zero
∀ {R : Type u_1} [inst : CommSemiring R] [Nontrivial R] {p : Polynomial R}, p.IsPrimitive → p ≠ 0- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNontrivial
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.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Cproof · cited by 1,598
- dvd_zeroproof · cited by 63
- IsUnit.ne_zeroproof · cited by 36
- Polynomial.IsPrimitivestatement and proof · cited by 33
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.primPart_ne_zeroproof · cited by 2
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0
- Polynomial.isPrimitive_iff_ne_zeroproof · cited by 0