Theorems · Definition · field theory
IntermediateField.extendScalars
{K : Type u_1} →
{L : Type u_2} →
[inst : Field K] →
[inst_1 : Field L] → [inst_2 : Algebra K L] → {F E : IntermediateField K L} → F ≤ E → IntermediateField (↥F) LIf F ≤ E are two intermediate fields of L / K, then E is also an intermediate field of
L / F. It can be viewed as an inverse to IntermediateField.restrictScalars.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement and proof · cited by 988
- Subfield.extendScalarsproof · cited by 17
Cited by26
Results whose statement or proof uses this declaration.
- IntermediateField.extendScalars.orderIsoproof · cited by 5
- IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraicstatement and proof · cited by 4
- IntermediateField.relrank_eq_rank_of_lestatement · cited by 3
- IntermediateField.extendScalars_restrictScalarsstatement · cited by 2
- IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraicstatement and proof · cited by 2
- IntermediateField.mem_extendScalarsstatement · cited by 1
- IntermediateField.extendScalars_le_extendScalars_iffstatement · cited by 1
- IntermediateField.extendScalars.orderIso_applystatement · cited by 0
- IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_leftstatement · cited by 0