Theorems · Theorem · field theory
Polynomial.SplittingField.adjoin_rootSet
∀ {K : Type v} [inst : Field K] (f : Polynomial K), Algebra.adjoin K (f.rootSet f.SplittingField) = ⊤- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Polynomial.rootSetstatement · cited by 101
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.IsSplittingField.adjoin_rootSetproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Gal.extproof · cited by 5
- GaloisField.finrankproof · cited by 2