Theorems · Theorem · commutative algebra
Field.DirectLimit.exists_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) {p : Ring.DirectLimit G f},
p ≠ 0 → ∃ y, p * y = 1- Defined in
- Mathlib.Algebra.Colimit.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Fieldstatement and proof · cited by 7,404
- IsDirectedOrderstatement and proof · cited by 316
- mul_inv_cancel₀proof · cited by 210
- RingHom.map_oneproof · cited by 76
- RingHom.map_zeroproof · cited by 47
- RingHom.map_mulproof · cited by 45
- Ring.DirectLimitstatement and proof · cited by 26
- Ring.DirectLimit.ofproof · cited by 21
- Ring.DirectLimit.induction_onproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Field.DirectLimit.invproof · cited by 2
- Field.DirectLimit.mul_inv_cancelproof · cited by 1