Theorems · Definition · field theory
IntermediateField.powerBasisAux
{K : Type u} →
[inst : Field K] →
{L : Type u_3} →
[inst_1 : Field L] →
[inst_2 : Algebra K L] → {x : L} → IsIntegral K x → Module.Basis (Fin (minpoly K x).natDegree) K ↥K⟮x⟯The elements 1, x, ..., x ^ (d - 1) form a basis for K⟮x⟯,
where d is the degree of the minimal polynomial of x.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Module.Basisstatement · cited by 1,477
- Polynomial.natDegreestatement · cited by 1,105
- IntermediateFieldstatement · cited by 988
- minpolystatement · cited by 439
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement · cited by 382
- AlgEquiv.toLinearEquivproof · cited by 117
- finCongrproof · cited by 78
- Module.Basis.mapproof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin.powerBasisproof · cited by 17