Theorems · Theorem · field theory
IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing
∀ {A : Type u_1} {B : Type u_2} [inst : Ring A] [IsSimpleRing A] [inst_2 : Field B] [IsAlgClosed B] (f : A →+* B)
(p : Polynomial A), (Polynomial.map f p).roots.card = p.natDegree- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.mapstatement · cited by 806
- Multiset.cardstatement · cited by 375
- Polynomial.rootsstatement · cited by 264
- IsAlgClosedstatement and proof · cited by 150
- IsSimpleRingstatement and proof · cited by 39
- Polynomial.natDegree_mapproof · cited by 21
- IsAlgClosed.card_roots_eq_natDegreeproof · cited by 4
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