Theorems · Theorem · commutative algebra
Polynomial.IsPrimitive.mul
∀ {R : Type u_1} [inst : CommRing R] [NormalizedGCDMonoid R] {p q : Polynomial R},
p.IsPrimitive → q.IsPrimitive → (p * q).IsPrimitive- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 112 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.
Cites14
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
- mul_oneproof · cited by 3,885
- IsUnitproof · cited by 1,602
- NormalizedGCDMonoidstatement and proof · cited by 159
- Associated.symmproof · cited by 87
- Polynomial.contentproof · cited by 41
- Polynomial.IsPrimitivestatement and proof · cited by 33
- normalize_eq_oneproof · cited by 10
- Polynomial.normalize_contentproof · cited by 8
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.IsPrimitive.content_eq_oneproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsPrimitiveRoot.minpoly_eq_powproof · cited by 1
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0