Theorems · Theorem · field theory
Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed
∀ (k : Type u) [inst : Field k] (K : Type v) [inst_1 : Field K] [IsAlgClosed K] [inst_3 : Algebra k K] (p q : Polynomial k), IsCoprime p q ↔ ∀ (a : K), (Polynomial.aeval a) p ≠ 0 ∨ (Polynomial.aeval a) q ≠ 0
- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFieldIsAlgClosedAlgebra
Around this declaration
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Cites23
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- map_mulproof · cited by 1,137
- Polynomial.mapproof · cited by 806
- Polynomial.evalproof · cited by 796
- Polynomial.aevalstatement and proof · cited by 615
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