Theorems · Theorem · commutative algebra
AdicCompletion.residueField_map_bijective_of_fg
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] (fg : (IsLocalRing.maximalIdeal R).FG),
Function.Bijective ⇑(IsLocalRing.ResidueField.map (algebraMap R (AdicCompletion (IsLocalRing.maximalIdeal R) R)))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- Submoduleproof · cited by 7,192
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- pow_oneproof · cited by 894
- Function.Bijectivestatement · cited by 863
- Ideal.mapproof · cited by 692
- Ideal.Quotient.mkproof · cited by 610
- IsLocalRingstatement and proof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.residueField_map_bijectiveproof · cited by 1