Theorems · Theorem · field theory
Polynomial.IsSplittingField.adjoin_rootSet
∀ {K : Type v} (L : Type w) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (f : Polynomial K)
[Polynomial.IsSplittingField K L f], Algebra.adjoin K (f.rootSet L) = ⊤- Cited by
- 7 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- 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.IsSplittingFieldstatement and proof · cited by 50
- Polynomial.IsSplittingField.adjoin_rootSet'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.IsSplittingField.finiteDimensionalproof · cited by 3
- Polynomial.SplittingField.adjoin_rootSetproof · cited by 2
- Polynomial.IsSplittingField.adjoin_rootSet_eq_rangeproof · cited by 1
- Normal.of_isSplittingFieldproof · cited by 0
- Polynomial.IsSplittingField.splits_iffproof · cited by 0
- Polynomial.IsSplittingField.mulproof · cited by 0
- Polynomial.IsSplittingField.of_algEquivproof · cited by 0