Theorems · Theorem · field theory
Polynomial.Monic.isUnit_leadingCoeff_of_dvd
∀ {R : Type u} [inst : CommRing R] [IsDomain R] {a p : Polynomial R}, p.Monic → a ∣ p → IsUnit a.leadingCoeff- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsDomainstatement and proof · cited by 2,196
- IsUnitstatement · cited by 1,602
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.leadingCoeffproof · cited by 101
- isUnit_of_dvd_oneproof · cited by 18
- Polynomial.leadingCoeff_dvd_leadingCoeffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Monic.irreducible_iff_degree_ltproof · cited by 1