Theorems · Theorem · field theory
Irreducible.not_isRoot_of_natDegree_ne_one
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} [IsDomain R],
Irreducible p → p.natDegree ≠ 1 → ∀ {x : R}, ¬p.IsRoot x- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement and proof · cited by 1,105
- Irreduciblestatement and proof · cited by 496
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.natDegree_eq_of_degree_eq_someproof · cited by 42
- Polynomial.degree_eq_one_of_irreducible_of_rootproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Irreducible.aeval_ne_zero_of_natDegree_ne_oneproof · cited by 0
- Irreducible.isRoot_eq_bot_of_natDegree_ne_oneproof · cited by 0