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Theorems · Theorem · commutative algebra

Field.DirectLimit.mul_inv_cancel

∀ {ι : Type u_1} [inst : Preorder ι] (G : ι → Type u_2) [inst_1 : Nonempty ι] [inst_2 : IsDirectedOrder ι]
  [inst_3 : (i : ι) → Field (G i)] (f : (i j : ι) → i ≤ j → G i → G j) {p : Ring.DirectLimit G f},
  p ≠ 0 → p * Field.DirectLimit.inv G f p = 1
Defined in
Mathlib.Algebra.Colimit.Ring
Cited by
1 results in Mathlib
Foundations
Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderNonemptyIsDirectedOrderField
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Around this declaration

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

Field.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.inv · cited by 2DirectLimit.invField.DirectLimit.exists_inv · cited by 1DirectLimit.exists_invDirectLimit.mul_inv_cancelCITED BYCITES

Cites6

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Cited by1

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