Theorems · Definition · field theory
Subfield.extendScalars
{L : Type u_2} → [inst : Field L] → {F E : Subfield L} → F ≤ E → IntermediateField (↥F) LIf F ≤ E are two subfields of L, then E is also an intermediate field of
L / F. It can be viewed as an inverse to IntermediateField.toSubfield.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 58 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- Subfieldstatement and proof · cited by 303
- Subfield.toIntermediateFieldproof · cited by 5
Cited by21
Results whose statement or proof uses this declaration.
- Subfield.relrankproof · cited by 40
- IntermediateField.extendScalarsproof · cited by 25
- Subfield.relfinrankproof · cited by 23
- Subfield.relrank_eq_rank_of_lestatement and proof · cited by 7
- Subfield.extendScalars.orderIsoproof · cited by 5
- Subfield.relrank_eq_of_inf_eqproof · cited by 4
- Subfield.relrank_mul_relrankproof · cited by 3
- Subfield.extendScalars_toSubfieldstatement and proof · cited by 2
- Subfield.extendScalars_selfstatement · cited by 1
- Subfield.extendScalars_topstatement and proof · cited by 1
- Subfield.mem_extendScalarsstatement · cited by 1
- Subfield.coe_extendScalarsstatement · cited by 0