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Theorems · Definition · commutative algebra

Field.DirectLimit.inv

{ι : Type u_1} →
  [inst : Preorder ι] →
    (G : ι → Type u_2) →
      [Nonempty ι] →
        [IsDirectedOrder ι] →
          [inst_3 : (i : ι) → Field (G i)] →
            (f : (i j : ι) → i ≤ j → G i → G j) → Ring.DirectLimit G f → Ring.DirectLimit G f

Noncomputable multiplicative inverse in a direct limit of fields.

Defined in
Mathlib.Algebra.Colimit.Ring
Cited by
2 results in Mathlib
Foundations
Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderNonemptyIsDirectedOrderField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Field.DirectLimit.mul_inv_cancel · cited by 1DirectLimit.mul_inv_cancelField.DirectLimit.inv_mul_cancel · cited by 0DirectLimit.inv_mul_cancelPreorder · cited by 7952PreorderField · cited by 7404FieldIsDirectedOrder · cited by 316IsDirectedOrderRing.DirectLimit · cited by 26Ring.DirectLimitField.DirectLimit.exists_inv · cited by 1DirectLimit.exists_invDirectLimit.invCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.