Theorems · Theorem · field theory
Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin
∀ {F : Type u_1} {K : Type u_2} {L : Type u_3} [inst : Field F] [inst_1 : Field K] [inst_2 : Field L]
[inst_3 : Algebra F K] [inst_4 : Algebra F L] [Algebra.IsAlgebraic F K],
IntermediateField.normalClosure F K L ≤ ⨆ x, IntermediateField.adjoin F ((minpoly F x).rootSet L)- Defined in
- Mathlib.FieldTheory.Normal.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- AlgHomproof · cited by 3,236
- iSupstatement and proof · cited by 2,415
- map_zeroproof · cited by 1,614
- IntermediateFieldstatement · cited by 988
- Polynomial.aevalproof · cited by 615
- AlgHom.toRingHomproof · cited by 490
- minpolystatement and proof · cited by 439
- IntermediateField.adjoinstatement and proof · cited by 382
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splitsproof · cited by 3
- Algebra.IsAlgebraic.algHomEmbeddingOfSplitsproof · cited by 0