Theorems · Theorem · commutative algebra
MvPolynomial.dvd_monomial_iff_exists
∀ {R : Type u_1} {σ : Type u_2} [inst : CommRing R] [NoZeroDivisors R] {p : MvPolynomial σ R} {n : σ →₀ ℕ} {a : R},
a ≠ 0 → (p ∣ (MvPolynomial.monomial n) a ↔ ∃ m b, m ≤ n ∧ b ∣ a ∧ p = (MvPolynomial.monomial m) b)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- mul_commproof · cited by 2,262
- MvPolynomialstatement and proof · cited by 2,140
- NoZeroDivisorsstatement and proof · cited by 545
- MvPolynomial.Cproof · cited by 400
- MvPolynomial.monomialstatement and proof · cited by 253
- map_dvdproof · cited by 44
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.irreducible_of_disjoint_supportproof · cited by 1
- MvPolynomial.dvd_smul_X_iff_existsproof · cited by 1
- MvPolynomial.dvd_monomial_one_iff_existsproof · cited by 0