Theorems · Theorem · commutative algebra
Polynomial.exists_primitive_lcm_of_isPrimitive
∀ {R : Type u_1} [inst : CommRing R] [NormalizedGCDMonoid R] {p q : Polynomial R},
p.IsPrimitive → q.IsPrimitive → ∃ r, r.IsPrimitive ∧ ∀ (s : Polynomial R), p ∣ s ∧ q ∣ s ↔ r ∣ s- 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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Cites47
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
- mul_oneproof · cited by 3,885
- Nontrivialproof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- pow_zeroproof · cited by 1,094
- le_transproof · cited by 985
- Polynomial.leadingCoeffproof · cited by 498
- sub_add_cancelproof · cited by 344
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