Theorems · Theorem · commutative algebra
MvPolynomial.dvd_C_iff_exists
∀ {R : Type u_1} {σ : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R] {f : MvPolynomial σ R} {a : R},
a ≠ 0 → (f ∣ MvPolynomial.C a ↔ ∃ b, b ∣ a ∧ f = MvPolynomial.C b)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- NoZeroDivisorsstatement and proof · cited by 545
- MvPolynomial.Cstatement and proof · cited by 400
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.totalDegreeproof · cited by 76
- map_dvdproof · cited by 44
- MvPolynomial.totalDegree_eq_zero_iff_eq_Cproof · cited by 9
- MvPolynomial.totalDegree_Cproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.dvd_monomial_iff_existsproof · cited by 3