Theorems · Theorem · field theory
Polynomial.mem_ker_modByMonic
∀ {R : Type u} [inst : CommRing R] {q : Polynomial R}, q.Monic → ∀ {p : Polynomial R}, p ∈ q.modByMonicHom.ker ↔ q ∣ p- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- LinearMap.kerstatement · cited by 848
- Polynomial.Monicstatement and proof · cited by 461
- LinearMap.mem_kerproof · cited by 66
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- Polynomial.modByMonicHomstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.ker_modByMonicHomproof · cited by 0