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Theorems · Theorem · field theory

AlgHom.fieldRange_toSubalgebra

∀ {K : Type u_1} {L : Type u_2} {L' : Type u_3} [inst : Field K] [inst_1 : Field L] [inst_2 : Field L']
  [inst_3 : Algebra K L] [inst_4 : Algebra K L'] (f : L →ₐ[K] L'), f.fieldRange.toSubalgebra = f.range
Defined in
Mathlib.FieldTheory.IntermediateField.Basic
Cited by
4 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldFieldAlgebraAlgebra
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Around this declaration

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

IntermediateField.LinearDisjoint.isDomain' · cited by 1LinearDisjoint.isDomain'IntermediateField.LinearDisjoint.isField_of_forall · cited by 0LinearDisjoint.isField_of…IntermediateField.fieldRange_comp_val · cited by 0IntermediateField.fieldRa…IntermediateField.LinearDisjoint.map'' · cited by 0LinearDisjoint.map''Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgHom · cited by 3236AlgHomSubalgebra · cited by 1353SubalgebraAlgHom.range · cited by 169AlgHom.rangeIntermediateField.toSubalgebra · cited by 134IntermediateField.toSubal…AlgHom.fieldRange · cited by 57AlgHom.fieldRangeAlgHom.fieldRange_toSubalgebraCITED BYCITES

Cites7

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Cited by4

Results whose statement or proof uses this declaration.