Mathlib Map

Theorems · Definition · field theory

Subfield.toSubring

{K : Type u} → [inst : DivisionRing K] → Subfield K → Subring K

Reinterpret a Subfield as a Subring.

Defined in
Mathlib.Algebra.Field.Subfield.Defs
Cited by
23 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
DivisionRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IntermediateField.adjoin · cited by 382IntermediateField.adjoinSubfield.map · cited by 30Subfield.mapSubfield.comap · cited by 29Subfield.comapSubfield.subtype · cited by 16Subfield.subtypeFixedPoints.minpoly · cited by 9FixedPoints.minpolySubfield.coe_sInf · cited by 5Subfield.coe_sInfSubfield.toIntermediateField · cited by 5Subfield.toIntermediateFi…Subfield.topologicalClosure · cited by 5Subfield.topologicalClosu…FixedPoints.minpoly.eval₂ · cited by 5minpoly.eval₂Subfield.lift_relrank_map_map · cited by 4Subfield.lift_relrank_map…FixedPoints.minpoly.monic · cited by 4minpoly.monicSubfield.copy · cited by 2Subfield.copySubfield.toAddSubgroup · cited by 2Subfield.toAddSubgroupFixedBy.intermediateField · cited by 2FixedBy.intermediateFieldSubfield.mem_iSup_of_directed · cited by 2Subfield.mem_iSup_of_dire…DivisionRing · cited by 1062DivisionRingSubring · cited by 602SubringSubfield · cited by 303SubfieldSubfield.toSubringCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by33

Results whose statement or proof uses this declaration.