Theorems · Theorem · field theory
IntermediateField.adjoin_rootSet_isSplittingField
∀ {K : Type v} {L : Type w} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {p : Polynomial K},
(Polynomial.map (algebraMap K L) p).Splits →
Polynomial.IsSplittingField K (↥(IntermediateField.adjoin K (p.rootSet L))) p- Cited by
- 0 results in Mathlib
- Foundations
- Depth 144 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.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IntermediateFieldstatement · cited by 988
- Polynomial.mapstatement and proof · cited by 806
- IntermediateField.adjoinstatement · cited by 382
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.rootSetstatement and proof · cited by 101
- IntermediateField.subset_adjoinproof · cited by 59
- Polynomial.IsSplittingFieldstatement · cited by 50
- IntermediateField.splits_of_splitsproof · cited by 5
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