Theorems · Definition · field theory
AlgebraicClosure.toSplittingField
{k : Type u} →
[inst : Field k] →
(s : Finset (AlgebraicClosure.Monics k)) →
MvPolynomial (AlgebraicClosure.Vars k) k →ₐ[k] (∏ f ∈ s, ↑f).SplittingFieldGiven a finite set of monic polynomials, construct an algebra homomorphism
to the splitting field of the product of the polynomials
sending indeterminates $X_{f_i}$ to the distinct roots of f.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- Finset.prodstatement · cited by 2,356
- MvPolynomialstatement · cited by 2,140
- Polynomial.Monicstatement · cited by 461
- MvPolynomial.aevalproof · cited by 298
- Polynomial.SplittingFieldstatement · cited by 42
- AlgebraicClosure.Monicsstatement and proof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicClosure.spanCoeffs_ne_topproof · cited by 1
- AlgebraicClosure.toSplittingField_coeffstatement and proof · cited by 1