Theorems · Theorem · field theory
Polynomial.rootSet_monomial
∀ {R : Type u} {S : Type v} [inst : Field R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra R S] {n : ℕ},
n ≠ 0 → ∀ {a : R}, a ≠ 0 → ((Polynomial.monomial n) a).rootSet S = {0}- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Setstatement and proof · cited by 53,352
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.rootSet_C_mul_X_powproof · cited by 1