Theorems · Theorem · field theory
Irreducible.isRoot_eq_bot_of_natDegree_ne_one
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} [IsDomain R], Irreducible p → p.natDegree ≠ 1 → p.IsRoot = ⊥- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement and proof · cited by 1,105
- Irreduciblestatement and proof · cited by 496
- Polynomial.IsRootstatement · cited by 152
- le_bot_iffproof · cited by 116
- Irreducible.not_isRoot_of_natDegree_ne_oneproof · cited by 2
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