Theorems · Theorem · field theory
IsAlgClosed.card_aroots_eq_natDegree_of_leadingCoeff_ne_zero
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : Field B] [IsAlgClosed B] [inst_3 : Algebra A B]
{p : Polynomial A}, (algebraMap A B) p.leadingCoeff ≠ 0 → (p.aroots B).card = p.natDegree- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Multiset.cardstatement · cited by 375
- IsAlgClosedstatement and proof · cited by 150
- Polynomial.arootsstatement · cited by 89
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