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Theorems · Theorem · field theory

IntermediateField.inv_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 : L}, x ∈ S → x⁻¹ ∈ S

An intermediate field is closed under inverses.

Defined in
Mathlib.FieldTheory.IntermediateField.Basic
Cited by
4 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra
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Around this declaration

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

IntermediateField.eq_adjoin_of_eq_algebra_adjoin · cited by 3IntermediateField.eq_adjo…IntermediateField.coe_iSup_of_directed · cited by 2IntermediateField.coe_iSu…toIntermediateField_toSubalgebra · cited by 0toIntermediateField_toSub…Field.isSeparable_inv · cited by 0Field.isSeparable_invAlgebra · cited by 11388AlgebraField · cited by 7404FieldIntermediateField · cited by 988IntermediateFieldInvMemClass.inv_mem · cited by 52InvMemClass.inv_memIntermediateField.inv_memCITED BYCITES

Cites4

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Cited by4

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