Theorems · Theorem · commutative algebra
MvPolynomial.C_dvd_iff_dvd_coeff
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (r : R) (φ : MvPolynomial σ R),
MvPolynomial.C r ∣ φ ↔ ∀ (i : σ →₀ ℕ), r ∣ MvPolynomial.coeff i φ- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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.
Cites19
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 and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- MvPolynomial.Cstatement and proof · cited by 400
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.monomialproof · cited by 253
- MvPolynomial.supportproof · cited by 220
Cited by3
Results whose statement or proof uses this declaration.
- map_wittStructureIntproof · cited by 13
- MvPolynomial.dvd_C_iff_existsproof · cited by 1
- MvPolynomial.C_dvd_iff_map_hom_eq_zeroproof · cited by 1