Theorems · Theorem · field theory
IntermediateField.algebraMap_mem
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (S : IntermediateField K L)
(x : K), (algebraMap K L) x ∈ SAn intermediate field contains the image of the smaller field.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.toSubalgebraproof · cited by 134
- Subalgebra.algebraMap_mem'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.isGaloisproof · cited by 13
- IntermediateField.adjoin.algebraMap_memproof · cited by 3
- IntermediateField.adjoin_inductionstatement and proof · cited by 2
- IntermediateField.sSup_toSubfieldproof · cited by 1
- IntermediateField.subset_adjoin_of_subset_leftproof · cited by 1
- IntermediateField.Lifts.exists_lift_of_splits'proof · cited by 1
- IntermediateField.sup_toSubfieldproof · cited by 1