Theorems · Theorem · field theory
IsAlgClosed.splits_domain
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [IsAlgClosed k] [inst_2 : Field K] {f : k →+* K} (p : Polynomial k),
(Polynomial.map f p).SplitsEvery polynomial splits in the field extension f : K →+* k if K is algebraically closed.
- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsAlgClosedField
Around this declaration
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Cites8
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
- IsAlgClosedstatement and proof · cited by 150
- IsAlgClosed.splitsproof · cited by 29
- Polynomial.Splits.mapproof · cited by 19
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