Theorems · Theorem · field theory
PerfectField.splits_of_natSepDegree_eq_one
∀ {E : Type v} [inst : Field E] {K : Type w} [inst_1 : Field K] [PerfectField K] {f : Polynomial E} (i : E →+* K),
f.natSepDegree = 1 → (Polynomial.map i f).Splits- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFieldPerfectField
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Cites9
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 and proof · cited by 806
- Polynomial.Splitsstatement · cited by 290
- Polynomial.natSepDegreestatement and proof · cited by 53
- PerfectFieldstatement and proof · cited by 36
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.natSepDegree_mapproof · cited by 1
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