Theorems · Theorem · commutative algebra
AdicCompletion.residueField_map_bijective
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsNoetherianRing R] [inst_2 : IsLocalRing R], Function.Bijective ⇑(IsLocalRing.ResidueField.map (algebraMap R (AdicCompletion (IsLocalRing.maximalIdeal R) R)))
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Function.Bijectivestatement · cited by 863
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- AdicCompletionstatement · cited by 160
- IsLocalRing.ResidueFieldstatement · cited by 156
- IsLocalRing.ResidueField.mapstatement · cited by 16
- Ideal.fg_of_isNoetherianRingproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.spanFinrank_maximalIdeal_eqproof · cited by 0