Theorems · Theorem · field theory
Irreducible.aeval_ne_zero_of_natDegree_ne_one
∀ {R : Type u} {S : Type v} [inst : CommRing R] [IsDomain R] [inst_2 : Ring S] [inst_3 : Algebra R S] [FaithfulSMul R S]
{p : Polynomial R},
Irreducible p → p.natDegree ≠ 1 → ∀ {x : S}, x ∈ (algebraMap R S).range → (Polynomial.aeval x) p ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
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- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement · cited by 3,236
- IsDomainstatement and proof · cited by 2,196
- map_zeroproof · cited by 1,614
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.evalproof · cited by 796
- Polynomial.aevalstatement · cited by 615
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