Theorems · Definition · field theory
Subfield.closure
{K : Type u} → [inst : DivisionRing K] → Set K → Subfield KThe Subfield generated by a set.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- DivisionRingstatement and proof · cited by 1,062
- InfSet.sInfproof · cited by 935
- Subfieldstatement and proof · cited by 303
Cited by43
Results whose statement or proof uses this declaration.
- IntermediateField.adjoinproof · cited by 382
- Subfield.subset_closurestatement · cited by 15
- Subfield.closure_lestatement and proof · cited by 8
- Subfield.gistatement and proof · cited by 6
- Subfield.closure_eqstatement · cited by 4
- IsFractionRing.ringHom_fieldRange_eq_of_comp_eqstatement and proof · cited by 3
- Subfield.cardinalMk_closure_le_maxstatement · cited by 3
- Subfield.closure_unionstatement · cited by 2
- IntermediateField.adjoin_inductionproof · cited by 2
- IntermediateField.restrictScalars_adjoin_of_algEquivproof · cited by 2
- IntermediateField.adjoin_toSubfieldstatement · cited by 2
- IsFractionRing.ringHom_fieldRange_eq_of_comp_eq_of_range_eqstatement and proof · cited by 2