Theorems · Theorem · field theory
Polynomial.Monic.C_dvd_iff_isUnit
∀ {R : Type u} [inst : CommSemiring R] {p : Polynomial R}, p.Monic → ∀ {a : R}, Polynomial.C a ∣ p ↔ IsUnit a- Defined in
- Mathlib.Algebra.Polynomial.Degree.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.Monicstatement and proof · cited by 461
- IsUnit.mapproof · cited by 104
- isUnit_iff_dvd_oneproof · cited by 21
- IsUnit.dvdproof · cited by 13
- Polynomial.Monic.coeff_natDegreeproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.degree_pos_of_not_isUnit_of_dvd_monicproof · cited by 2